# How do you differentiate f(x) = xcos((pix)/2) using the chain rule?

Feb 24, 2016

This problem actually requires BOTH the chain rule and the product rule ...

#### Explanation:

$f ' \left(x\right) = \cos \left(\frac{\pi x}{2}\right) + x \left(- \sin \left(\frac{\pi x}{2}\right) \times \frac{\pi}{2}\right)$

Now simplify, ...

$\cos \left(\frac{\pi x}{2}\right) - \frac{\pi x}{2} \sin \left(\frac{\pi x}{2}\right)$

Hope that helped