Understanding Derivatives and the Product Rule

The video tutorial explains how to find the derivative of a function F(x) = x^5 * G(x) using the product rule. Given values for G(2) and G'(2), the tutorial demonstrates the step-by-step process to calculate F'(2). The product rule is reviewed, and the derivative of each component is found. Substituting the given values, the final result for F'(2) is calculated as -112, which represents the slope of the tangent line at x = 2.

What is the value of G(2) given in the problem?

• -3

• 4

• 5

• 2

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

• Chain Rule

• Product Rule

• Quotient Rule

• Sum Rule

In the product rule, what is the derivative of the first function multiplied by?

• The first function

• The derivative of the first function

• The second function

• The derivative of the second function

What is the derivative of x to the 5th power?

• x^5

• 4x^5

• 5x^5

• 5x^4

What is the first step in calculating F'(2)?

• Calculate G(2)

• Find G'(2)

• Substitute 2 for x

• Differentiate F(x)

What is the value of 2 to the 5th power?

• 128

• 64

• 16

• 32

What is the result of multiplying 32 by 4 in the calculation of F'(2)?

• 128

• 32

• 64

• 256

What is the value of G'(2) used in the calculation?

• -3

• 5

• 4

• 2

What is the final value of F'(2)?

• -112

• 112

• 0

• 240

What does F'(2) represent in terms of the graph of F(x)?

• The y-intercept

• The minimum point

• The slope of the tangent line at x = 2

• The maximum point