Originally Posted by

**kmjt** I have some confusion relating the chain rule and product rule when differentiating sinusoidal functions compared to when I used the rules comfortably when it was just regular functions. I am aware that the derivative of sinx is cosx, and that the derivative of cosx is -sinx btw.

**Example 1:**

f(x)=sin(sinx)

Would this be the product rule? If so would it look like:

f'(x)=(cosx)(sinx)+(sinx)(cosx)

however the book answer is f'(x)=[cos(sinx)](cosx)

What am I doing wrong?

**Example 2:**

f(theta)= (-pi/2 sin)(2theta-pi)

product rule? and would the derivative of -pi/2sin be -pi/2cosx?