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 first step in applying the product rule to a function involving arctan?

• Multiply the entire function by its derivative

• Identify the inverse function and differentiate it

• Multiply by the square root of the function

• Apply the chain rule first

When applying the product rule, what is the derivative of the square root of x?

• x^2

• 1/2 * x^(-1/2)

• 2x

• x^(1/2)

How can you express x^(1/2) in terms of fractions?

• x^(1/3)

• 1/x

• x^2

• x^(1/2)

What is a key reason for simplifying expressions in calculus problems?

• To avoid using the product rule

• To prepare for multiple-choice tests

• To ensure they fit on a single line

• To make them look more complex

What happens when you divide fractions in the context of simplifying expressions?

• You divide the numerators

• You multiply the fractions

• You add the exponents

• You subtract the exponents