What is the derivative of \cot^2(x) ?

Pam Stokes

Pam Stokes

Answered question

2021-12-18

What is the derivative of cot2(x) ?

Answer & Explanation

Foreckije

Foreckije

Beginner2021-12-19Added 32 answers

You would use the chain rule to solve this. To do that, youll
Edward Patten

Edward Patten

Beginner2021-12-20Added 38 answers

f(x)=cot2x
df(x)dx=2cotx(csc2x)
=2csc2xcotx
first you get the derivative of the indice, then the trig function, lastly the x.
it's easy if you remember it that way ;)

RizerMix

RizerMix

Expert2021-12-29Added 656 answers

I like the previous answer, but I think it's simpler to use the product rule. Since
cot2x=cotxcotx, ddx(cot2x)=f(x)g(x)+g(x)f(x) where
f(x)=g(x)=cotx. This evaluate to
cotx×(1sin2x)+(1sin2x)×cotx=2(1sin2x)cotx2cotxsin2x
This is equivalent to the previous answer, since 1sin2x=csc2x, but I think that that answer is cleaner, don't you?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?