Chain rule

The chain rule applies to functions that take in another function as input. Let's consider , which is often written as  and read as f of g of x. This means that the output of g(x) will become the input to the function f.

The derivative of this will be written as follows:

This is the same as . 

For example, suppose we have  and . We then differentiate the two functions and get  and .

By plugging this into the preceding formula, we get .