# How to Find a Function's Derivative by Using the Chain Rule

The chain rule is by far the trickiest derivative rule, but it’s not really that bad if you carefully focus on a few important points.

By the way, here’s one way to quickly recognize a composite function.

Whenever the argument of a function is anything other than a plain old *x*, you’ve got a composite function.

Here’s how to differentiate it with the chain rule:

You start with the outside function (the square root), and differentiate that, IGNORING what’s inside.

To make sure you ignore the inside, temporarily replace the inside function with the word

*stuff.*Multiply the result from Step 1 by the derivative of the inside function,

*stuf**f**´*.Take a good look at this.

*All*basic chain rule problems follow this basic idea. You do the derivative rule for the outside function, ignoring the inside*stuff*, then multiply that by the derivative of the*stuff*.Differentiate the inside

*stuff*.Put the real

*stuff*and its derivative back where they belong.Simplify.