Apply the product rule of taking the derivative with sine

The video tutorial explains how to identify and label two functions, find their derivatives, and apply the product rule to solve a problem. The instructor uses F of X and G of X as labels and demonstrates the process of finding derivatives and applying the product rule step-by-step. The tutorial emphasizes the importance of writing expressions correctly and provides tips for simplifying calculations.

How is the expression for the derivative structured in the text?

What simplification is suggested for writing the expression involving cosine of X?