In some occasions, Chain Rule can be applied instead of Product Rule. Look at the example below:

Find the derivative of f(x)=sec³x

If you use product rule, you will get (secx*tanx)*secx*tanx+secx(secx*tanx)+secx*secx*(secx*tanx)=3sec³x*tanx

But that uses more time than just doing a simple chain rule. Here, f(x) can be think of the composition of two functions -- a secant function and a function to the 3rd power.

 

So by using chain rule instead, we get this:

f'(x)=3sec²x*(secx*tanx)=3sec³x*tanx