Understanding the Chain Rule

The video tutorial introduces the chain rule in calculus, starting with its abstract formula. It then demonstrates how to apply the chain rule in a concrete example, specifically finding the derivative of a composite function. The tutorial explains the process of defining functions f(x) and g(x), applying the power rule, and calculating the derivative of f' of g(x). The video concludes with a review of the steps involved in using the chain rule to find derivatives.

What is the main purpose of the chain rule in calculus?

• To find the derivative of a product of two functions

• To find the derivative of a quotient of two functions

• To find the integral of a function

• To find the derivative of a composition of two functions

In the example provided, what is the function f(x) defined as?

• x to the power of 3

• x minus 3

• The square root of x

• 3x squared minus x

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is the function g(x) in the example?

• x squared

• 3x squared minus x

• The square root of x

• x plus 3

How is the derivative of f(g(x)) expressed using the chain rule?

• f'(x) * g'(x)

• f'(g(x)) * g'(x)

• f(x) * g(x)

• f'(x) + g'(x)

What is the derivative of f(x) when f(x) is the square root of x?

• x to the power of -1/2

• 1/2 * x to the power of 1/2

• x to the power of 1/2

• 1/2 * x to the power of -1/2

What is the derivative of g(x) when g(x) is 3x squared minus x?

• 6x minus 1

• 3x squared

• x minus 3

• 6x plus 1

What is the final expression for the derivative of the composition f(g(x))?

• 1/2 * g(x) to the power of -1/2 * g'(x)

• g(x) to the power of 1/2 * g'(x)

• 1/2 * g(x) to the power of 1/2 * g'(x)

• g(x) to the power of -1/2 * g'(x)

What is the conceptual understanding of the chain rule?

• It finds the derivative of a sum of functions

• It finds the derivative of a product of functions

• It finds the integral of a function

• It finds the derivative of a composition of functions

What is the role of the power rule in the chain rule application?

• It helps find the integral of a function

• It helps find the derivative of a function raised to a power

• It helps find the derivative of a quotient of functions

• It helps find the derivative of a product of functions

What is the derivative of the outer function in the example?

• g(x) to the power of 1/2

• x to the power of -1/2

• 1/2 * x to the power of 1/2

• 1/2 * g(x) to the power of -1/2