Understanding Derivatives and the Product Rule

The video tutorial explains how to evaluate the derivative of the product of two functions, F and H, at x=3. It introduces the values of the functions and their derivatives at this point. The tutorial then demonstrates the application of the product rule to find the derivative of the product of these functions. Finally, it calculates the derivative at x=3 using the given values, resulting in a final value of 24.

What is the value of F(3) as given in the problem?

• 0

• 9

• 3

• 6

What is the derivative of H at X=3?

• 2

• 4

• 6

• 8

What is the task that needs to be performed with the functions F(x) and H(x)?

• Evaluate the derivative of their product at X=3

• Determine the maximum value of H(x)

• Find the sum of F(x) and H(x)

• Calculate the integral of F(x)

What is the product rule used for?

• Calculating the derivative of a product of two functions

• Solving differential equations

• Finding the sum of two functions

• Integrating a single function

Which of the following is part of the product rule formula?

• f'(x) * h(x) + f(x) * h'(x)

• f(x) / h(x)

• f(x) * h(x)

• f'(x) + h'(x)

What is the first term in the product rule application for G'(3)?

• F(3) * H'(3)

• F'(3) + H'(3)

• F(3) + H(3)

• F'(3) * H(3)

What is the value of the first term in the product rule application for G'(3)?

• 12

• 6

• 24

• 0

What is the second term in the product rule application for G'(3)?

• F(3) + H(3)

• F'(3) + H'(3)

• F(3) * H'(3)

• F'(3) * H(3)

What is the value of the second term in the product rule application for G'(3)?

• 0

• 12

• 24

• 36

What is the final result of G'(3) after applying the product rule?

• 36

• 24

• 12

• 0