Let's not beat around the bush. Here you go:

Pretty amazing that the derivative of an ugly function like would be a pretty function like . It's kind of a Cinderella story for functions, but without the pumpkins, glass slipper and raging royal hormones.

Now, suppose that we want to differentiate . We have two options:

**Option 1:** Just do it by the chain rule .

**Option 2:** Use the fact that

Then,

In general, the chain rule says

So for instance,