Understanding the Chain Rule in Differentiation

The video tutorial explains how to find the derivative of a composite function using the chain rule. It starts by defining G(x) as F(x) raised to the 5th power and provides values for F(4) and F prime of 4. The tutorial emphasizes recognizing G(x) as a composite function and applying the chain rule, which involves differentiating the outer function and multiplying by the derivative of the inner function. The video concludes with a step-by-step calculation of G prime of 4, resulting in -810.

What is the outer function in the composite function G(x) = (F(x))^5?

• The power function

• x

• 5

• F(x)

Which rule is essential for finding the derivative of a composite function?

• Sum Rule

• Product Rule

• Quotient Rule

• Chain Rule

In the chain rule, what do you multiply the derivative of the outer function by?

• The integral of the inner function

• The second derivative of the outer function

• The derivative of the inner function

• The original function

If U = F(x), what is the derivative of U^5 according to the chain rule?

• 5U^4

• 5U^4 * U'

• U^5 * U'

• 5U^5

What is the value of F(4) given in the problem?

• 2

• 3

• 4

• 5

What is the value of F'(4) given in the problem?

• 2

• -2

• 0

• -1

What is the result of 3 raised to the 4th power?

• 9

• 243

• 81

• 27

What is the final value of G'(4) after calculation?

• -405

• 810

• 405

• -810