Question #a9f26

1 Answer
Jan 7, 2018

#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)#