Answer
$ -sin(x)$
Work Step by Step
We are given that $cos(x) = sin(\frac{\pi}{2}-x)$. It is also true that $sin(x) = cos(\frac{\pi}{2}-x)$ as the sine of an angle is the cosine of the complementary angle and vice versa.
We apply the chain rule:
$\frac{d}{dx} cos(x) = \frac{d}{dx} sin(\frac{\pi}{2}-x) = cos(\frac{\pi}{2}-x)*(\frac{d}{dx} [\frac{\pi}{2} -x]) = -cos(\frac{\pi}{2}-x) = -sin(x)$
