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School Education Karnataka

School Education Karnataka

Karnataka TET Hall Ticket 2020 {New Exam Date} www.schooleducation.kar.nic.in KARTET 2019 Exam Date

School Education Karnataka,www.schooleducation.kar.nic.in Karnataka Teacher Eligibility Test(TET) Hall Ticket 2020, Exam Date Postponed Check Here { New Exam Date* }: The Karnataka, School Education Board will be releasing the TET admit card in the month of July 2020. Department will upload the Kar TET 2020 Hall Ticket in July 2020 on the official web portal www.schooleducation.kar.nic.in. Those students who are going to appear Karnataka Teacher Eligibility Test can able to check their TET admit cards through this web page with the help of their login details or given below mention direct link http://schooleducation.kar.nic.in/index.html

Kar TET Hall Ticket 2020

Latest Update- KARTET- 2019 Examination to be held on 15-03-2020 has been further postponed until July 2020. Please download Hall ticket before the examination.

July: Latest Update Coming Soon, Keep visiting this Page Regularly.

School Education Karnataka
School Education Karnataka

Released Here >>> CBSE 10th & 12th Rechecking/Revaluation Form 2020
Karnataka TET Hall Ticket 2020

School Education Karnataka A few months before the Karnataka School Education Board had released the notification of Karnataka Teacher Eligibility Test for Teacher Posts (Classes 1st to 5th & 6th to 8th). The application form process has completed on 25th February 2020 by the organization. After filling the application form all the candidates start to look at their exam hall and exam date here and there through the internet. The Karnataka TET has been further postponed as per the government instructions due to the outbreak of Covid 19. As per the official notification, authority is going to conduct the Teacher Eligibility Test (TET) Paper I & Paper II in July at the various center and admit card/hall ticket will be available on the official web portal few days prior to the exam. Candidates stay and connected with us regarding the latest update.

 

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Karnataka TET New Exam Date 2020 Admit Card

 

Overview of Karnataka Teacher Eligibility Test KARTET Exam 2019-20 Details

Organization NameKarnataka School Education Board
Known AsKSEB
Exam NameKarnataka Teacher Eligibility Test
Vacancy NameTeacher (Classes 1 to 5 & 6 to 8)
Application Form Last date25th February 2020
Date of ExaminationJuly 2020
Article CategoryExam Admit Card
StatusAvailable Soon
Admit Card Issue DateAvailable Soon
Official Web sitewww.schooleducation.kar.nic.in

www.schooleducation.kar.nic.in TET Hall Ticket 2020

School Education Karnataka,The Massive number of candidates have applied in TET Application Form on or before the last date. All those candidates who applied will be appearing for the exam at various examination centers. Now all the candidates are eagerly waiting for their Kar TET Hall Ticket 2020. As you all know exams have been postponed now it is expected Admit Card will be released in the month of July Because the Authority is going to conduct the TET examination in July 2020. So don’t waste their precious time and start their exam preparation according to the exam schedule. When authority will be released exam TET 2020 Admit Card Karnataka on the official web portal then we will inform you through this web page. After that aspirants can able to check their exam call letters with the help of their login details.

Exam Pattern For TET Exam Paper 1 & 2

Paper 1 Exam Pattern

TopicsNumber of QuestionsTotal marksDuration
Child Development & Pedagogy30302.30 Hours
Language 13030
Language 23030
Mathematics3030
Environmental Studies3030
Social Studies (For Visually Impaired Candidates
Instead of EVS & Mathematics)
6060
Total150 Questions150 Marks

 

 

Paper 2 Exam Pattern

TopicsNumber of QuestionsTotal marksDuration
Child Development & Pedagogy (Compulsory)30302.30 hours
Language 1 (Compulsory)3030
Language 2 (Compulsory)3030
Mathematics & Science (Only for Mathematics
& Science Teacher)
6060
Social Studies (Only for Social Studies Teacher)6060
Total150150

KARTET 2019-20 Admit Card Download Online

School Education Karnataka, All the candidates are informed that the Karnataka Teacher Eligibility Test Exam Hall Ticket is very important for each and every candidate who is going to the examination. Without exam hall ticket examiner not allowed to enter inside the examination hall. So it is necessary to download and carry on the day of examination. Exam call letter contains various information such as exam venus and candidates information. Those candidates who are going to the examination can able to check and download their Kar TET Hall Ticket 2020 through given below mention direct link with the help of their application form registration number and date of birth wise. Her we provided some simple steps or links as given below mention you can follow it.

FAQs on Karnataka TET

Q1. When will the hall ticket for KTET be released?

Ans. Hall ticket for KTET will be released in July 2020.

Q2. What documents do I need to carry in the KTET exam?

Ans. During the KTET exam make sure to carry Hall Ticket, Admit Card along with any valid ID proof like Driving License, Voter ID, Pan Card, Adhar Card, etc.


JAC 12th Result Released Here >>> www.jac.jharkhand.gov.in 2020 Class 12

Q3. When will the Karnataka TET exam be conducted?

Ans. Authorities will conduct the Karnataka TET exam in July 2020.

How to download Karnataka TET Exam Hall Tickets 2020 Online

Step 1: Candidates visit the official web site of School Education Karnataka i.e. www.schooleducation.kar.nic.in

Step 2: Home Page will appear on the screen.

Step 3: Scroll Down the home page and click on the link for KARTET Hall Ticket 2019-20.

Step 4: Enter Application Number and Date of Birth.

Step 5: Click on the submit button and your admit card will appear on the screen.

Step 7: Save it and take a print out for future use it.

School Education Karnataka,

Important Link

Official Website Click Here

Admit Card Link   Click Here

Notice All India Certificate www.allcertificate.in

Indgovtjobs

Government Jobs Notification 22 May 2020

Indgovtjobs

Indgovtjobs,India Government Jobs IndGovtJobs 2019/2020: Find All India Government Jobs Notifications, Results, Admit Card, Application Forms and more on,IndGovtJobs website where you can find Central Government, State Government, Bank Jobs, Railway Jobs and General Knowledge. IndGovtJobs,Ind Govt Jobs. 128K likes. IndGovtJobs is one of the leading Indian Govt Jobs Employment News Provider And Govt Jobs In Punjab

Latest July 2020 Jobs

 

Indgovtjobs
Indgovtjobs

 

More Informations

All India Certificate Informations www.allcertificate.in

Indgovtjobs


Indgovtjobs hello friends welcome freegovtjoobalert.net Website   here is one famous course back do what you love and the money will follow you but for (Indgovtjobs )debt have to learn some things after the meat I think you have to do something and then you do something when you dare to do somethings I will say that bottle side with him who dear once again welcome to our channel it’s possible.

 

no I will like to share with you some jobs which are right now preparing you 2080 and which are going on to three very soon so there is first one better certification ingenious international limited in Sea Island the last day to apply is 31st March of 2015 and the qualification is vacancy that isB II level V V Tech called civil mechanical electrical and instrumentation with 50% at least math they are planning to be direct in terms of selection and if you want to see the advertisement.

then they have given advertisement in employment newspaper also the salary will be ranging fromtwenty thousand six hundred to 46,500 security right space so thank theseapply to those vacancies second one is mangalore refinery and petrochemical limited that is mr peter mr period is looking for eligibleindian nationals for various second supposition the last day to apply of22nd April of 2008 P  (Indgovtjobs ) since they had demanded being file and fire and 60pteams are true chemicals petroleum chemistry and environmental science theyare recruiting to return to follow with your interview and here salary is 60,000one Lake 18,000 or month the third vacancy is this aim that is audience todo medical science primarily to tell physician.

they have announced recruitment always in C in Group A B andC position or regular basis the last things to apply 26 March of 2018 theyare recruiting junior engineers je in electrical grants so you must have B orwe take electrical vanch the speller is thirty-five thousand fourhundred to one like 12,400 that is your seven please Kate what one is nationaland momentum and gene earning Research Institute that is you and Lilly SIA SIAand we all know that Nene has been established in that year 1958 right nowit is having certain vacancy on various Ohthe last edge to apply is second April 2015they are demanding 4v between chemical engineering environmental engineering ormechanical engineering.

if you want to see the further detailing you can visittheir site www.mediaed.org this is ranging from forty four thousand nine hundred to specific thousand one hundred with beyond p dr. McKenzie is at Oslothat is your true face application at Spa SSD and the bar they are recruiting scientist engineer s be the last P to apply is psyching apparel of 2018 theyare demanding to PhD Emmy and (Indgovtjobs ) B we take in concern visiting me in electronicsVLSI or microwaves the salary is ranging from 60 7702 to like 87,000 for furtherdetails you can do it there and the bus by the second one is P and PSD that if your Tamil nadu Public Service Commission their last day to apply is 20set so I 26 March of 2018.

we are eclipsing a sustained ingeniousmainly be we take in civil structural engineeringliterally engineering electronics and communication communication engineeringand electrical engineering they are giving the seventh pay scale that is34800 if you are great pay of 5100 okay the next vacancy that is your second Mayseventh of a can see is that bei ve l that is Bharat Electronics Limited BLhas 30 vacancy of electronic engineer with no experience and for utilityengineering computer science and electronics  (Indgovtjobs )with minimum one yearexperience the knob three to apply is your 4th April of 2018 pay scale will befrom 40,000 to one leg 40,000 per half the vacancy number 8 which is right nowvery popular SB is that is Bureau of Indian Standard recruitment in 2018 they’re recruiting 100 vacancy at scientist V position.

you required mechanical engineering metallurgical engineering civil engineering electrical electronic engineering chemical engineering even good technology and textile and fiber – today’s the last day to apply is 2nd April of 2018 the salary will be starting from seventy nine thousand nine hundred twenty nine done second last vacancy that is a value thank you I can see is West Bengal new civil service commission that is Amethyst they have published recruitment for the position of service strength ingenious in mechanical bond that is 57 vacancy input safety officers imposition of foot inspector they are recruiting three officer (Indgovtjobs ) they have demanded for degree in food technology daily technologies biotech oil take and agricultural side the last day to apply is 16 of rail of 2018 and the salary will start from ten thousand forty thousand five hundred per month with a grandpa of 4400 a when a spike in sales Maharashtra vacancy that is MP psv maharani finger they invite online application.

before till 31st March 2018 educational qualification is graduate and civil civil and Dada and construction engineering selection will be returned followed by your personal (Indgovtjobs ) interviews and the salary will be ranging from fifteen thousand six hundred to twenty four thousand eight hundred we can grant a office thousand five hundred per month if you want to visit the further detail toucan feel this side www dot and P as P dot govt dots in so kind o you have enjoyed this all valuable in the information.

Legal Heir Certificate| legal heir certificate in India

 Legal Heir Certificate succession certificate

Legal Heir Certificate,What is the succession certificate, what is the way to make it and when is it made, if your father or your grandfather has passed away and they have no will, then you may not have easy ownership of their property. In such a situation, the succession certificate office succession certificate is necessary for you to get the rights on the property, because this certificate proves that you are the legal heir and after the father’s death, you have acquired the ownership of the property. What rights can an heir have? The heir can actually claim ownership over the property of a deceased person according to the law. The deceased person who is in it is deposited in his bank account Fixed Deposit Share Mutual Fund

 Legal Heir Certificate succession certificate
 Legal Heir Certificate succession certificate

Gets your ownership over all other types of investments that are involved. Let you talk. In the area where the property of the deceased person of the application form is present, a recording of the application was submitted in the civil court with a format. Goes in which the heir has to mention all the property on which he is supposed to own, in this application, he should have the liver of all the heirs, after this, the date and place of the death of the deceased person, in full, is also detailed. Along with this, a copy of the death certificate is also put, after that, after submitting an application, the court issues an advertisement to this effect according to the public notice in the newspaper, along with the notice is sent to all the parties. Whether or not objections are invoked in the court means that if someone has objections, then they can raise their objections in the court

Can tell that within 45 days after the issue of this notice, if no one has any objection, if they do not submit their objection in the court or if someone is objecting, then they should also submit a document in support of it. It happens that after 45 days of the issue of the notice, the court issues the certificate to the person applying, if any objections have been made or if the petition has been challenged, then the process may be delayed in issuing the certificate. Court fees are also required to be paid, which is according to the property of a deceased person. The person applying for the certificate has to pay this amount in the form of Judicial stamp paper. The succession certificate is a mandatory document. But it is not enough just to get the property of a dead person, apart from the need of other things, it has a death certificate i.e.

There is also a need for a certificate. If the application to get the ticket is not challenged, then the court usually issues the certification certificate in five 7 months, then again a small video has come on the above certificate that now you have understood that What is the succession certificate

Sample Format Download For Legal Heir Certificate

Download Now Sample Format 

Govt Official Websites 

Apply Online 

 

The following persons are considered legal heirs and can claim a legal heir certificate under Indian Law:

  • Spouse of the deceased
  • Children of the deceased (Son/ Daughter)
  • Parents of the deceased
  • Sibling of the deceased

How Uses of Legal Heir Certificate ?

The Use Of Legal Heir certificate -As stated above, a legal heir certificate identifies the rightful successor who then, can claim the assets/properties of the deceased person. All eligible successors must possess this certificate to lay a claim over the deceased person’s property.

Legal heir certificate is required  purpose:

  1. For transferring properties and assets of the demised person to his successors.
  2. For claiming insurance.
  3. For sanctioning and processing family pension of the deceased employee.
  4. To receive dues such as provident fund, gratuity etc from the Government
  5. To receive salary arrears of the deceased, state or central Government employee.
  6. To gain employment based on compassionate appointments.

Generally, for any property purchase or registration, the buyer should request for a legal heir certificate to ascertain the ownership of the property. There can be instances, where there are several legal heirs for an ancestral property and in such cases, it is required that all legal heirs sign on the deed of conveyance giving their approval to avoid any litigations.

Procedure to Obtain Legal Heir Certificate

Legal Heir certificate can be obtained by approaching the area/taluk Thasildhar, or from the corporation/municipality office of the respective area, and from the district civil court. This certificate names all legal heirs’ of the deceased person and is issued only after a proper enquiry. Listed below are the steps involved in the process of obtaining a legal heir certificate:

  1. The legitimate heir of the deceased person must approach the appropriate authority in the respective area
  2. with a signed application. This application should contain the names of all the legal heirs, their relationship with the deceased and addresses of the family members. The death certificate of the departed person should also be attached. (Death certificate must be obtained from the municipality/corporation office)
  3. An affidavit on stamp paper has to be submitted.
  4. Revenue Inspector/administrative officer conducts an inspection and completes the enquiry.
  5. Once the enquiry is completed successfully, the authorized officer issues the Legal heir certificate

The process of obtaining a legal heir certificate generally takes 30 days. If there is an unnecessary delay in receiving this certificate or the concerned authorities fail to respond, you should then approach the Revenue Division Officer(RDO)/sub-collector.

Documents Required

In order to obtain a legal heir certificate, following is the list of documents required:

  1. Signed application form
  2. Identity/Address proof of the applicant
  3. Death certificate of the deceased
  4. Date of Birth proof of all legal heirs
  5. A self-undertaking affidavit
  6. Address proof of the deceased

Note:

  • Identity Proof of Applicant can be voter’s ID, Aadhaar Card Driving License, Passport or any other government-issued identity card.
  • Address proof of legal heir can be any valid identity proof or telephone/mobile bill, gas bill, bank passbook with the name and address of the legal heir
  • Date of birth proof of legal heir can be a birth certificate, school transfer/leaving certificate, PAN card, passport etc.

Explicit Formula | geometric sequence formula

Explicit Formula-How explicit formulas work

Explicit Formula,An explicit formula designates the nth term of the sequence, as an expression of n (where n = the term’s location). It defines the sequence as a formula in terms of n

Here is an explicit formula of the sequence 3, comma, 5, comma, 7, comma, point, point, point
a, left parenthesis, n, right parenthesis, equals, 3, plus, 2, left parenthesis, n, minus, 1, right parenthesis
In the formula, n is any term number and a, left parenthesis, n, right parenthesis is the n, start superscript, start text, t, h, end text, end superscript term.
This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term.
In order to find the fifth term, for example, we need to plug n, equals, 5 into the explicit formula.
\begin{aligned}a(\greenE 5)&=3+2(\greenE 5-1)\\\\ &=3+2\cdot4\\\\ &=3+8\\\\ &=11\end{aligned}
Cool! This is in fact the fifth term of 

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Equivalent explicit formulas

Explicit formulas can come in many forms.
For example, the following are all explicit formulas for the sequence 3, comma, 5, comma, 7, comma, point, point, point
  • 3, plus, 2, left parenthesis, n, minus, 1, right parenthesis (this is the standard formula)
  • 1, plus, 2, n
  • 5, plus, 2, left parenthesis, n, minus, 2, right parenthesis
The formulas may look different, but the important thing is that we can plug an n-value and get the correct n, start superscript, start text, t, h, end text, end superscript term (try for yourselves that the other formulas are correct!).
Different explicit formulas that describe the same sequence are called equivalent formulas.

Explicit Formula A common misconception

An arithmetic sequence may have different equivalent formulas, but it’s important to remember that only the standard form gives us the first term and the common difference.
For example, the sequence 2, comma, 8, comma, 14, comma, point, point, point has a first term of start color #0d923f, 2, end color #0d923f and a common difference of start color #ed5fa6, 6, end color #ed5fa6.

The explicit formula start color #0d923f, 2, end color #0d923f, start color #ed5fa6, plus, 6, end color #ed5fa6, left parenthesis, n, minus, 1, right parenthesis describes this sequence, but the explicit formula start color #0d923f, 2, end color #0d923f, start color #ed5fa6, plus, 6, end color #ed5fa6, n describes a different sequence.

In order to bring the formula 2, plus, 6, left parenthesis, n, minus, 1, right parenthesis to an equivalent formula of the form A, plus, B, n, we can expand the parentheses and simplify:
\begin{aligned}&\phantom{=}2+6(n-1)\\\\ &=2+6n-6\\\\ &=-4+6n\end{aligned}
Some people might prefer the formula minus, 4, plus, 6, n over the equivalent formula 2, plus, 6, left parenthesis, n, minus, 1, right parenthesis, because it’s shorter. The nice thing about the longer formula is that it gives us the first term.

Explicit Equation for Exponential Growth

Explicit Formula
Explicit Formula
A Population Grows According to An Exponential Growth Model. The Initial Populations P Sub 0 = 16 And The Growth Rate Is R = 0.35. Which Means The Growth Rate would Be 35%. So Every End Unit Of Time the Population Grows Or Increases By 35%.
But For The Recursive And explicit Formulas Given Here, We Do Need To Use The Decimal form Of The Growth Rate. So For The Recursive Formula We Would Have P Sub N= The Quantity 1 + R That Would Be 1 + 0.35 Sowed Have 1.35 X P Sub And – 1.
So Now When We Find P Sub 1,n = 1, So I’ll Substitute 1 Whereas Well As Here. So P Sub 1 Is = To 1.35x P Sub 1 – 1 That Would Be P Sub Which We Know Is Equal To 16. So 1.35 X 16 = 21.6.so P Sub 1 = 21.6. Now When We Find P Sub 2,n = 2. So We’ll Have 1.35 X P Sub 2 – that’s P Sub 1, Which We Just Found. That’s Equal To 21.6. And Now We’ll Go Back to The Calculator 1.35 X 21.6 = 29.16. Notice When Using the Recursive Formula To Find The Next Value Of P We Always Use The Previous value Of P.
Next We’re Asked To Find The explicit Formula For P Sub N, Which Is Given Hereford Exponential Growth. P Sub N = P Sub 0 X The Quantity + R Raise To The Power Of N. And We Already Have All the Information We Need. P Sub 0 = 16and R = 0.35.
So We Have P Sub N = P Sub which Is 16 X The Quantity 1 + R Which Is 1.35raise To The Power Of N. Now We Can Use Our Explicit formula To Find P Sub 11 Without Knowing P Sub 10. P Sub 11 Is = To 16x 1.35 Raise To The Power Of 11. So 16 X 1.35raise To The Power Of 11. Our Directions Do Say Round Toat Least 1 Decimal Place. So If Round To The Tenths, Notice How We Have A 0in The Hundredths So This Would Be approximately 434.3. I Hope You Found This Helpful.

Derivative of Secx

Derivative of Secx

Sec(x) Derivative Rule

Secant is the reciprocal of the cosine. The secant of an angle designated by a variable x is notated as sec(x).
The derivative rule for sec(x) is given as:

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants sec x —1 and m and n are integers): Sec X + sec x —1 Let f (x) = sec x +1 Let u — — sec x So, f'(x) = Using quotient rule – sec x +1
Derivative of Secx
Derivative of Secx

let’s find the derivative…

of the secant of x.

How would we go about doing this?

Well sec(x) is another way of writing 1/cos(x)…

and since we have a quotient here,

the quotient rule would aptly apply…

so written in short hand, the quotient rule is:

y-dash or y-prime… I’m going to call it y-dash…
is equal to (vu’ – uv’) / v^2.

And in this case, we have y = sec(x), and…

I’m going to let u equal the numerator of 1

and v equal the denominator: cos(x).

So now if we apply the quotient rule…

for the first part, we have v, so cos(x) remains unchanged…

multiplied by the derivative of u.

So the derivative of 1, a constant, is zero…

then minus u, which is one, times the derivative of v…

which is the derivative of cos(x)…

and that’s equal to -sin(x)…

all over v^2, which is cos^2(x).

So the result is positive sin(x)…

divided by the cos^2(x).

And I can rewrite this as…

[sin(x)/cos(x)]*1/cos(x).

And then I can realise that this part is equal to…

the tangent of x… and this part is equal to again…

the secant of x!

So the derivative of sec(x) is equal to…

tan(x)*sec(x)

 

Derivative of sec(x)

Sec(x) Derivative Rule

Secant is the reciprocal of the cosine. The secant of an angle designated by a variable x is notated as sec(x).
The derivative rule for sec(x) is given as:

ddxsec(x) = tan(x)sec(x)

This derivative rule gives us the ability to quickly and directly differentiate sec(x).
X may be substituted for any other variable.
For example, the derivative ddysec(y) = tan(y)sec(y), and the derivative ddzsec(z) = tan(z)sec(z).

Proof of the Derivative Rule

The sec(x) derivative rule is originates from the relation that sec(x) = 1/cos(x). Now, the first step of finding the derivative of 1/cos(x) is using the quotient rule.

Using the quotient rule on 1/cos(x) gives us:
[sin(x)/cos(x)][1/cos(x)]
sin(x)/cos(x) = tan(x), and 1/cos(x) = sec(x)
Therefore, it simplifies to tan(x)sec(x), resulting in:
ddxsec(x) = tan(x)sec(x)

Derivative Rules of the other Trigonometry Functions

Derivative Rules Here’s the derivative rules for the other five major trig functions:
ddxsin(x) = cos(x)
ddxcos(x) = -sin(x)
ddxtan(x) = sec2(x)
ddxcot(x) = -csc2(x)
ddxcsc(x) = -cot(x)csc(x)

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Antiderivative of secxtanx
Antiderivative of secxtanx

We have to find the antiderivative of secx tanx. To find the antiderivative of secx
tanx we must first understand the meaning or definition of antiderivative.
Antiderivative is an operation which is opposite of derivation operation that
means antiderivative calculates the integral of a derivative.
Suppose we have a function f(x), its derivative is g(x) means d(f(x))= g(x) than
antiderivative of g(x) is f(x) that is J g(x) dx = f(x) + c dx. So we get f(x) as
antiderivative of g(x) is a constant.
We have understood the meaning of antiderivative, so now we will calculate the
antiderivative of secx tanx.
Know More About Rational Number Multiplicative Inverse Worksheets
The process of finding antiderivative of sec(x) tan(x) is shown in steps below-
Step 1 : Find the derivative of sec(x), that is d(sec x) / dx = sec(x) tan(x) dx.
Therefore g(x) sec(x) tan(x).
Step 2 : Now to find the antiderivative of sec(x) tan(x) , we will have to find the
integral of sec(x) tan(x).
That is Jsec(x) tan(x) dx = sec(x).
Proof of above operation- => Let g(x)= sec x tan x dx => g(x) = J sin x / cos 2 x
dx ( sec x = I / cos x , tan x = sin x / cos x) Let u = cosx
Therefore du – sin x dx g(x) – f 1 / u 2 du g(x) – u-2 du g(x) = 1/
u + C => g(x) = 1/ cos x + C => g(x) sec x + C Hence proved. Here we have
used method of integration by parts to calculate the antiderivative of sec x tan x.
Hence to find the antiderivative of secxtanx we have to calculate the integral of

Derivative of Tanx

Derivative of Tanx

Derivative of Tanx,I want to differentiate derivative of tanx. How am I going to do this? Well, hopefully you remember that tangent theta is sine theta over cosine theta. Why is this? If you think back to the business about the right triangles, right, sine is this opposite side that I’m calling y over the hypotenuse.

Derivative of Tanx
Derivative of Tanx

And cosine is this adjacent side whose length I’ll call x over the hypotenuse. I’ll call this angle theta. Then sine theta is y over r, and cosine theta is x over r, so this fraction can be simplified to y over x. That’s the opposite side over the adjacent side. That’s tangent of theta.

Derivative of Tanx

So good. I can express Tangent theta as sin theta over cosine theta, how does that help? Well, I know how to differentiate sine and cosine, and by writing tangent this way, tangents now a quotient, so I can use the. Quotient rule. All right, so I’ll use the quotient rule, and the derivative of tangent theta is the derivative of the numerator, which is cosine, times the der, denominator, which is just cosine, minus the derivative of the denominator, which is minus sine, times the numerator, which is sine.

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Derivative of Tanx

And this whole thing is over the denominator squared, cosine squared theta. Now, is this very helpful? Well, I’ve got cosine times cosine, so I can write that as cosine squared theta. And here I’ve got minus negative sine theta times sine theta, so that ends up being plus sine squared theta. And the whole thing is still being divided by cosine squared theta. (Derivative of Tanx) Can I simplify that at all? Well cosine squared plus sine squared, that’s the Pythagorean identity. That’s just one. So I can replace the numerator with just one, still over cosine squared theta. And one over cosine squared theta, well, one over cosine is called secant, so this is really secant squared theta. . So what all this shows is the derivative of tangent theta is second squared theta.

A moment ago we did a calculation using the quotient rule to see that the derivative of tangent theta is second squared theta. And now I want to see how this plays out in some concrete example to get a, a real sense as to why a formula like this is true. So here’s a couple triangles. They’re both right triangles and the length of their hypotenuse is the same. This angle I am calling alpha, let’s this be a (Derivative of Tanx) little bit less than 45 degree. And this angle I am calling beta, and it’s more than 45 degrees. Now what you can say about the Secant of alpha and the Secant of beta? You know, the Secant of alpha is definitely bigger than one. I mean, what’s the Secant? It’s this hypotenuse length divided by this length here. And that’s bigger than one. How does it compare to beta? Well, the secant of beta is quite a bit bigger than the secant of alpha, and why is that? Well,

the secant of beta is this length here, the hypotenuse, divided by this width, but this triangle is quite a bit narrower than this triangle. So the secant has the same numerator, the hypotenuse, the same length, but the denominator here is quite a bit smaller, and if the denominator’s a lot smaller, then the ratio, which is the secant, is quite a bit bigger. Some of the secan of beta is bigger than the secan of alpha, and the secan of alpha is bigger than one. And that means that secan squared alpha is also (Derivative of Tanx) bigger than one. And secan squared alpha is less than secan squared beta. And the significance of that is right here, the derivative of tangent theta is secan squared theta. So what does this mean? Well, this, this is telling me how wiggling theta affects tangent. It affects it like a factor of secant squared theta. So in this example, where secant squared beta is a lot bigger than secant squared alpha, the effect of wiggling beta on the tangent of beta should be a lot larger than the effect of wiggling alpha on the tangent of alpha. And you can see that. Let me draw a triangle, where I’ve wiggled the angle alpha up a little bit. I’ve made it a little bit bigger. But I’m going to make the same hypotenuse.

 

All right, so this hypotenuse length is the same as this length, but I’ve made the angle a little bit bigger. And how is the tangent of the slightly larger alpha compared to the tangent of alpha. Well, the tangent of the slightly larger alpha is bigger than tangent alpha, but not by all that much. Now compare that to when I wiggle beta up by the same amount. I make beta a little bit bigger. Right. So I (Derivative of Tanx) make beta a little bit bigger by the same amount that I made alpha larger. And I think about how that affects the tangent of beta. The tangent of beta is this height divided by, divided by this width. And you can think about it, I mean this, this height maybe isn’t increasing a whole lot. But the width of this triangle is getting quite a bit narrower. And because it’s the ratio of that height to that width the tangent of the perturbed value of beta is quite a bit larger than the tangent of beta. And you can, you know it’s reflected in the fact the secant squared beta is a lot larger than secant squared alpha. So these, these kind of facts, right? The fact that the derivative of tangent is (Derivative of Tanx) secant squared theta you, you can really get a sense for why these things might be true by thinking about triangles and how wiggling the angle will affect certain ratios of sides of the triangles. But, if this seems a little too abstract we can kind of pull back a little bit and do do a numeric example next. You know, and maybe the numerical

example is sort of another

way to see a formula like this in action. Let’s do a numerical example to get a sense as to what you might do with the fact that the derivative of tangent is secen squared. Here’s an example, let’s try to approximate the value of tangent of 46 degrees. Why is this an interesting example? Well, we know the tangent of 45 degrees exactly, all right. And figure that out by looking at a triangle, here’s the angle, (Derivative of Tanx) 45 degrees, a right triangle, because the an, angles add up to, 180 degrees. So it’s 45 plus 90 plus what? Well, this must also be 45. It’s an isosceles triangle now, so these two sides are the same. A tangent is the ratio of this side to this side because they are equal that ratio was one. So I know the tangent of 45 exactly. It’s one.

 

But I am trying to figure out an approximation for the tangent of 46 degrees, the derivative tells me how wrigly an input affects the output, so I can use this fact and the fact that I know the derivative to try to approximate the tangent of 46. In particular the tangent of 46 degrees is the tangent of 45 plus one degree. And here you can see how I am perturbing the input a bit. And this is exactly (Derivative of Tanx) what the derivative would tell me something about. A little bit of bad news, the derivative of tangent is only secant squared if I do the measurement in radians. If I convert this to a problem in radians. With radians, says the tangent of pi/4, which is 45 degrees, plus with one degree in radians, is pi/180 radians, right? This is what I want to compute. I want to compute the tangent of pi/4 plus pi/180. And I’ll do that with approximation using the derivative. So according to the derivative this is about the tangent of pi over four, which is the tangent of 45 degrees, it’s one.

 

Plus the derivative of pi over four, which is secant squared pi over four. Times how much I wiggled the input by, which is pi over 180. I know the tangent of pi over four. It’s one. What’s the secant of pi over four squared? Well, if I pretend that these sides have length one, by the pythagorean theorem, this side must have length square root of two. The secant is hypotenuse over this width.

 

So the secant of pi over four is square root of two. So secant squared pi over four is square root of two squared, which is two times pi over 180. Now if you know an approximation for pi, you can compute two times pi over 180 plus one. And this is approximately 1.0349, and it keeps (Derivative of Tanx) going Pi’s irrational. And this is not so far off of the actual value. If we actually compute tangent of 46, the actual value is about 1.0355 and it keeps going. And· 1 0355. is awfully close to 1.0349. So we’ve successfully used the derivative to approximate the value of tangent 46 degrees.

Derivative Proof of tan(x)

Derivative proof of tan(x)

We can prove this derivative by using the derivatives of sin and cos, as well as quotient rule.

Write tangent in terms of sine and cosine

Take the derivative of both sides

Use Quotient Rule

Simplify

Use the Pythagorean identity for sine and cosine

and simplify

Derivative of Tanx
Derivative of Tanx

Derivative proofs of csc(x), sec(x), and cot(x)

The derivative of these trig functions can be obtained easily from the Qoutient Rule using the reciprocals of sin(x), cos(x), and tan(x).

The basic trigonometric functions include the following 6 functions: sine (sinx), cosine (cosx), tangent (tanx), cotangent (cotx), secant (secx) and cosecant (cscx).

All these functions are continuous and differentiable in their domains. Below we make a list of derivatives for these functions.

Derivatives of Basic Trigonometric Functions

We have already derived the derivatives of sine and cosine on the Definition of the Derivative page. They are as follows:

(sinx)=cosx,(cosx)=sinx.

Using the quotient rule it is easy to obtain an expression for the derivative of tangent:

(tanx)=(sinxcosx)=(sinx)cosxsinx(cosx)cos2x=cosxcosxsinx(sinx)cos2x=cos2x+sin2xcos2x=1cos2x.

The derivative of cotangent can be found in the same way. However, this can be also done using the chain rule for differentiating a composite function:

(cotx)=(1tanx)=1tan2x(tanx)=1sin2xcos2x1cos2x=cos2xsin2xcos2x=1sin2x.

Similarly, we find the derivatives of secant and cosecant:

(secx)=(1cosx)=1cos2x(cosx)=sinxcos2x=sinxcosx1cosx=tanxsecx,

(cscx)=(1sinx)=1sin2x(sinx)=cosxsin2x=cosxsinx1sinx=cotxcscx.

Derivative of Tanx
Derivative of Tanx

Derivative of Tanx Solved Problems

Click or tap a problem to see the solution.

Example 1

y=cos2x2sinx

Example 2

y=tanx+13tan3x

Example 3

y=cosx13cos3x

Example 4

y=1cosnx

Example 5

y=sinx1+cosx

Example 6

y=cos2sinx

Example 7

y=xsinx+cosx

Example 8

y=sin2x

Example 9

y=cos1x

Example 10

y=sin3x+cos3x

Example 11

y=tanx2cotx2

Example 12

y=x2sinx+2xcosx2sinx

Example 13

y=tan2x+lncos2x

Example 14

y=sinnxcosnx

Example 15

y=ln1sinx1+sinx

Example 16

Calculate the derivative of the functiony=(2x2)cosx+2xsinxat x=π.

Example 17

Calculate the derivative of the functiony=(x+1)cosx+(x+2)sinxat x=0.

Example 18

y=sec2x2+csc2x2

Example 19

y=(tanx)cosx,where0<x<π2.

Example 20

y=sin2x1+cotx+cos2x1+tanx