Prove that `d/(dx) (cot(x)) = -csc^2(x)`

Textbook Question

Chapter 3, 3.3 - Problem 19 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

Educator Approved

Educator Approved
kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

`d/(dx) (cot(x))`

`=d/(dx) (cos(x)/sin(x))`

`= ( ((cosx *(d/(dx) sin x)) -((d/(dx) cos x * sinx)))/(sin^2 x)`

`= (-cos^2 x -sin^2 x)/(sin^2 x)`

`= - 1/(sin^2 x)`

`= -csc^2(x)`

We’ve answered 318,936 questions. We can answer yours, too.

Ask a question