# What is the derivative of #cos(pi x)#?

##### 1 Answer

#### Explanation:

Here, we have a function inside another function (function composition). The outside function is

That means we can view

In order to find the derivative of a function composition, we must use the chain rule, which states if we have a function

Another way of "reading" this is to say that when differentiating, first differentiate the *outside* function while leaving the *inside* function intact, and then multiply that by the *derivative* of the inside function.

Here, we see that the derivative of the outside function,

Or, we can use

#f(x)=cos(x)=>f'(x)=-sin(x)# #g(x)=pix=>g'(x)=pi# ,

So if

#y'=f'(g(x))*g'(x)=-sin(pix)*pi=-pisin(pix)# .