Question

find f '(x) for f(x)=sqrt(sin(8x))

Answer 1

I will use the chain rule to solve this problem:

d/dx sqrt(sin(8x)) = (1/2)(sin(8x))^-(1/2) * d/dx(sin(8x))
= (1/2)(sin(8x))^-(1/2) * cos(8x) * d/dx 8x
= (1/2)(sin(8x))^-(1/2) * cos(8x) * 8
= 4cos(8x)/sqrt(sin(8x))

Let me know if any steps are unclear, I am happy to go into more detail.

Answer 2

thank you!!