Derivatives Inside of Derivatives

As you would imagine, finding a derivative is not limited to the basic rule forms. Some functions will require the use of multiple derivative rules to complete the full derivative. You will start to see derivative problems that are essentially derivatives inside derivatives.

The key to solving more advanced derivatives is to start by identifying your primary derivative rule. This primary derivative rule then allows you to start breaking a large derivative down into bite-size pieces. You then look at those bite-size pieces as their own little math problem, and identify the derivative rule you would need to use on that bite-size piece.

Unfortunately, there is not an order of operations for derivatives that you can follow to tell you what derivative to do first.