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