Derivative product rule with inverse tangent

The video tutorial explains the product rule in calculus, focusing on its application to functions involving the arctan and square root. The instructor guides students through the process of applying the product rule, simplifying expressions, and understanding the importance of presenting answers in a simplified form for different types of assessments. The tutorial emphasizes the need to recognize and simplify expressions for multiple-choice tests and provides correct answers for practice problems.

What is the product rule in calculus, and why is it important?

Explain the significance of the inverse function of tangent in the context of the given text.

How do you simplify the expression involving the square root of X and the product rule?

What steps are involved in finding the derivative of the function mentioned in the text?

Discuss the importance of recognizing how to simplify or evaluate expressions in calculus.