Chain rule with radicals, how to take the derivative

The video tutorial explains the process of finding the derivative of a composite function using the chain rule. It begins with identifying the parent and inside functions, F(x) and G(x), and proceeds to apply the chain rule to find the derivative. The tutorial provides a step-by-step calculation, including converting X sqrt to X to the 1/2, and concludes with the final derivative expression and its alternative forms.

What is the role of the inside function in the chain rule?

• It is the function that is differentiated first.

• It is the function that remains unchanged.

• It is the function that is differentiated last.

• It is the function that is ignored in the chain rule.

How can the square root of X be expressed in terms of exponents?

• X to the power of 1/2

• X to the power of -1/2

• X to the power of 2

• X to the power of 3/2

What is the derivative of X to the power of 1/2?

• 1/2 times X to the power of -1/2

• 2 times X to the power of 1/2

• 1/2 times X to the power of 1/2

• 2 times X to the power of -1/2

In the chain rule, what is the expression for F'(G(x))?

• G(x) times F'(x)

• G'(x) times F(x)

• F'(G(x)) times G'(x)

• F'(x) times G(x)

How can the expression 1/2 times sqrt(3X - 2) be rewritten?

• 2/3 times (3X - 2) to the power of 1/2

• 3/2 times sqrt(3X - 2)

• 1/2 times (3X - 2) to the power of 1/2

• 1/3 times sqrt(3X - 2)