Use the product rule to take the derivative of an exponential equation

The video tutorial explains the product rule in calculus, demonstrating how to take the derivative of a product of functions. It covers the steps involved, including taking derivatives of individual functions and simplifying the resulting expression by factoring. The tutorial also highlights the importance of recognizing factoring opportunities, especially in multiple-choice scenarios.

Describe the relationship between the first and second functions mentioned in the text.

What is the final expression derived from the calculations in the text?