Understanding the Power Rule for Derivatives

This video tutorial focuses on the power rule for derivatives, explaining how to apply it to various functions. It covers examples of differentiating monomials, constants, rational functions, and radical functions using the power rule. The video also provides practice problems to help viewers master the topic.

What is the first derivative of x squared using the power rule?

• x^2

• 2x

• 2x^2

• x

Using the power rule, what is the derivative of x cubed?

• x^2

• x^3

• 3x^2

• 3x

What is the derivative of x to the fourth power?

• 4x^3

• x^4

• 4x^4

• x^3

How do you find the derivative of a constant like 4?

• x

• 4

• 0

• 1

What is the derivative of 1 over x using the power rule?

• x

• -x^2

• 1/x

• -1/x^2

What is the derivative of 1 over x squared?

• 2/x^2

• -2/x^3

• -1/x^2

• 1/x^3

How do you express the square root of x in exponent form?

• x^2

• x^0

• x^1

• x^1/2

What is the derivative of the square root of x?

• 2√x

• √x

• 1/(2√x)

• 1/√x

How do you convert the fourth root of x cubed to exponent form?

• x^3

• x^4/3

• x^3/4

• x^1/4

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

• 1/(2x^1/2)

• x^1/2

• x

• 2x^1/2