How to use the product rule to take the derivative with trig functions with trig functions

The video tutorial explains the product rule in calculus, demonstrating how to differentiate a product of two functions. It provides a step-by-step application of the rule using specific functions, highlighting the importance of correctly handling negative signs. The tutorial emphasizes common mistakes students make, such as forgetting the negative sign in trigonometric functions, and offers tips for simplifying expressions.

Discuss the importance of the negative sign in the derivative of G of X.

How does the presence of X^3 in the expression affect the simplification of H prime of X?