Calculus Derivatives and Rules

This video tutorial covers higher order derivatives, focusing on the application of the power rule, chain rule, and quotient rule. It provides step-by-step solutions to derivative problems involving polynomial, exponential, and trigonometric functions. The video concludes with an invitation for viewers to ask questions for future videos.

What is the power rule for finding the derivative of x^n?

• n * x^(n-1)

• x^n

• n * x^n

• x^(n-1)

What is the derivative of 5x^4 using the power rule?

• 20x^3

• 4x^5

• 5x^3

• x^4

What is the second derivative of 5x^4?

• 5x^4

• 20x^3

• 60x^2

• x^2

How do you find the derivative of a composite function using the chain rule?

• Divide the derivative of the outer function by the inner function

• Add the derivatives of the outer and inner functions

• Subtract the derivative of the inner function from the outer function

• Multiply the derivative of the outer function by the derivative of the inner function

What is the derivative of (2x + 3)^(1/2) using the chain rule?

• (1/2)(2x + 3)^(-1/2) * 2

• (2x + 3)^(-1/2)

• (1/2)(2x + 3)^(1/2)

• (2x + 3)^(1/2)

What is the second derivative of (2x + 3)^(1/2)?

• -(1/2)(2x + 3)^(-3/2) * 2

• (1/2)(2x + 3)^(-1/2)

• (2x + 3)^(1/2)

• (2x + 3)^(-3/2)

What is the derivative of 4 - x to the power of -1?

• -(4 - x)^(-2)

• (4 - x)^(-1)

• -(4 - x)

• (4 - x)^2

What is the derivative of e^(ax)?

• a * e^(ax)

• e^(ax)

• a^2 * e^(ax)

• e^(a)

What is the second derivative of e^(ax)?

• e^(ax)

• a^3 * e^(ax)

• a * e^(ax)

• a^2 * e^(ax)

What is the quotient rule for derivatives?

• (uv' - u'v) / v^2

• (uv' + u'v) / v^2

• (u'v - uv') / v^2

• (u'v + uv') / v^2