Understanding Derivatives with the Power Rule

The video tutorial provides practice on taking derivatives using the power rule. It begins with a simple example of finding the derivative of 1/x by rewriting it as x to the negative power. The tutorial then moves on to finding the derivative of the cube root of x, demonstrating the power rule's application to fractional exponents. Finally, a more complex example is tackled, involving the derivative of the cube root of x squared, and evaluating it at a specific point. The tutorial emphasizes the versatility and power of the power rule in handling various derivative problems.

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

• x^2

• -x^-2

• x^-1

• -x^2

How can 1/x be rewritten to apply the power rule?

• x^1

• x^2

• x^0

• x^-1

What is the power rule formula for derivatives?

• n * x^(n-1)

• x^n

• n * x^(n+1)

• x^(n-1)

What is the derivative of x^n according to the power rule?

• n * x^(n-1)

• x^n

• x^(n-1)

• n * x^(n+1)

What is the derivative of x^2 using the power rule?

• 2x

• x^2

• 2x^2

• x

What is the derivative of the cube root of x?

• 1/3 * x^(-2/3)

• 3 * x^(1/3)

• x^(2/3)

• 1/3 * x^(2/3)

How can the cube root of x be expressed to use the power rule?

• x^(1/3)

• x^(3/2)

• x^(1/2)

• x^(2/3)

What is the derivative of x^(2/3)?

• x^(1/3)

• 3/2 * x^(1/3)

• 2/3 * x^(1/3)

• 2/3 * x^(-1/3)

How do you evaluate the derivative of the cube root of x squared at x = 8?

• 1/3

• 1/2

• 3/2

• 2/3

What is the result of 8^(1/3)?

• 1

• 4

• 2

• 3