Understanding Derivatives and Product Rule

The video tutorial explains how to find the derivative of a function defined as the product of two other functions, F and G, using the product rule. It evaluates the derivative at x = -1 by calculating the values of F, F', G, and G' at that point. The tutorial demonstrates the application of the product rule and the power rule to find the necessary derivatives, leading to the final result of F'(-1) = -8.

What is the value of F at negative 1?

• 4

• 3

• 2

• 1

What is the value of F prime at negative 1?

• 4

• 6

• 3

• 5

What is the function G of X?

• X

• X cubed

• X squared

• 1 over X

Which rule is used to find the derivative of a product of two functions?

• Product Rule

• Sum Rule

• Chain Rule

• Quotient Rule

What is the expression for capital F prime of X using the product rule?

• F of X times G of X

• F prime of X times G of X plus F of X times G prime of X

• F of X times G prime of X

• F prime of X times G of X

What is G of negative 1?

• 2

• 0

• -1

• 1

How do you express G of X in terms of exponents?

• X squared

• X

• X to the power of 1

• X to the power of -1

What is the derivative of G, G prime of X, using the power rule?

• Negative X to the power of 2

• X to the power of -2

• X to the power of 2

• Negative X to the power of -2

What is the value of G prime at negative 1?

• -1

• 2

• 1

• 0

What is the final value of F prime at negative 1?

• -7

• -8

• -5

• -6