Using the chain rule to take the derivative of an exponential equation

The video tutorial explains how to find the derivative of an exponential function using the chain rule. It starts by identifying the inside function, which can be represented in different notations. The tutorial then applies the chain rule, taking the derivative of the outside function and multiplying it by the derivative of the inside function. The example used is e to the 5x, resulting in a derivative of 5 times e to the 5x.

Explain the process of applying the chain rule as described in the text.

What is the final expression for the derivative mentioned in the text?