Question

Question #a9f26

Answer 1

`f'(x)=-(cot(sqrtx)csc(sqrtx))/(2sqrtx)`

Explanation:

Let's assume that you meant `f'(x)` instead of `f^!(x)`.
We use chain rule and then power rule for this problem.

First, remember that the derivitive of `f(x)=csc(x)` is `-cot(x)csc(x)`
MAKE SURE YOU UNDERSTAND WHY!

Also, remember that if `f(x)=x^y`, then `f'(x)=yx^(y-1)`

Therefore, `f'(x)=-cot(sqrtx)csc(sqrtx)*1/2x^-(1/2)` or `f'(x)=-(cot(sqrtx)csc(sqrtx))/(2sqrtx)`