Understanding Derivatives

This video tutorial covers the basics of finding derivatives using the power rule, including examples with polynomial, square root, rational, and absolute value functions. It explains the constant and multiple rules, and how to handle derivatives of rational functions and roots. The video also discusses the derivative of absolute value functions and their piecewise nature.

What is the derivative of x raised to the 4th power using the power rule?

• x^3

• 4x^4

• 3x^4

• 4x^3

How do you find the derivative of a constant like 7?

• 7x

• 7

• 0

• 1

What is the derivative of 5x using the power rule?

• x

• 0

• 5

• 1

How do you rewrite 1/x to apply the power rule for derivatives?

• x^1

• x^-1

• 1/x^2

• x^2

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

• 2x^2

• -2x^2

• 2x^(-3)

• -2x^(-3)

How do you express the square root of x in terms of exponents?

• x^(1/2)

• x^(-2)

• x^2

• x^(-1/2)

What is the derivative of the cube root of x^5?

• 3/5 x^(2/3)

• 5/3 x^(5/3)

• 3/5 x^(5/3)

• 5/3 x^(2/3)

How is the absolute value function of x represented in a piecewise form?

• x for x > 0, -x for x < 0

• -x for x > 0, -x for x < 0

• -x for x > 0, x for x < 0

• x for x > 0, x for x < 0

What is the derivative of the absolute value function for x > 0?

• 1

• -1

• 0

• x

What is the derivative of the absolute value function for x < 0?

• x

• 1

• -1

• 0