Understanding Composite Functions and Derivatives

The video tutorial explains how to find the derivatives of composite functions Big F and Big G using the chain rule and power rule. It starts by defining the functions and given values, then explains the concept of composite functions. The tutorial proceeds with a detailed derivation of Big F Prime and Big G Prime, applying the chain rule and power rule respectively. The explanation is aimed at helping viewers understand the process of finding derivatives of composite functions.

What is the expression for Big F of X?

• F of X to the fourth power

• F of X cubed

• F of X to the fifth power

• F of X squared

What is the value of F of 'A' given in the problem?

• 5

• 4

• 3

• 2

Which rule is used to find the derivative of composite functions?

• Chain Rule

• Quotient Rule

• Product Rule

• Power Rule

In the chain rule, what do you do after finding the derivative of the outer function?

• Add the derivative of the inner function

• Evaluate it at the inner function

• Multiply by the derivative of the outer function

• Divide by the inner function

What is the derivative of the inner function for Big F?

• 3X cubed

• 3X to the fourth power

• 3X squared

• 3X

What is the value of Big F Prime of 'A'?

• 180

• 45

• 90

• 135

What is the outer function for Big G?

• F of X

• X cubed

• X squared

• X to the fourth power

Which rule is used to find the derivative of Big G?

• Sum Rule

• Product Rule

• Quotient Rule

• General Power Rule

What is the value of F of 'A' squared?

• 8

• 12

• 16

• 20

What is the final value of Big G Prime of 'A'?

• 72

• 96

• 120

• 48