Derivative: chain rule applied to $\cos(\pi x)$ 
What is the derivative of the function $f(x)= \cos(\pi x)$? 

I found the derivative to be $f^{\prime}(x)= -\pi\sin(\pi x)$. Am I correct? Can you show me how to find the answer step by step? 
This is a homework question:

What is $x$ equal to if $-\pi\sin(\pi x)=0$?


The Chain Rule: If $g$ is differentiable at $x$ and $f$ is differentiable at $g(x)$, then the composite function $F=f\circ g$ defined by $F(x)=f(g(x))$ is differentiable at $x$ and $F'$ is given by the product $$F'(x)=f'(g(x))\cdot g'(x).$$
If $f(x)=cos(\pi x)$, then $f'(x)-sin(\pi x)\cdot \pi=-\pi sin(\pi x)$.
If $-\pi sin(\pi x)=0$, then $x=n$ where $x\in \mathbb{Z}$.
