Understanding Function Composition and Derivatives

The video tutorial explains how to evaluate the derivative of a composite function using the chain rule. It begins by listing the values of functions f and g and their derivatives at specific x values. The tutorial then defines the composition of functions and applies the chain rule to find the derivative of the composite function. Finally, it demonstrates the calculation of f prime of 4 using given values.

What values are provided in the table for functions f and g?

• Values of f and g at x=0 and x=1

• Values of f and g at x=-1 and x=5

• Values of f and g at x=-2 and x=4

• Values of f and g at x=2 and x=3

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CCSS.HSF-BF.A.1C

How is the function F defined in terms of f and g?

• F is the difference of f and g

• F is the composition of f and g

• F is the product of f and g

• F is the sum of f and g

What mathematical rule is applied to evaluate the derivative of a composite function?

• Product Rule

• Power Rule

• Quotient Rule

• Chain Rule

What is the first step in applying the chain rule to find F'(4)?

• Find f'(4)

• Find g'(4)

• Find f(4)

• Find g(4)

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CCSS.HSF.IF.A.2

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

• 2

• -2

• 4

• 0

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CCSS.HSF.IF.A.2

What is the value of f'(-2) used in the calculation of F'(4)?

• 3

• 2

• 1

• 0

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CCSS.HSF.IF.A.2

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

• 10

• 6

• 4

• 8

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CCSS.HSF-BF.A.1C

What is the final value of F'(4) after applying the chain rule?

• 4

• 6

• 8

• 10

Which of the following is NOT a step in applying the chain rule?

• Differentiate the outer function

• Multiply by the derivative of the inner function

• Add the derivatives of the functions

• Substitute the inner function's value

What is the purpose of using the chain rule in this problem?

• To find the integral of a function

• To find the product of two functions

• To find the derivative of a composite function

• To find the sum of two functions