Power Rule and Derivatives

The video tutorial reviews the power rule of differentiation combined with the chain rule. It explains how to find the derivative of a function U raised to the power of n with respect to X, where U is a function of X. An example is provided with the function F(x) = 3 * (4x - 7)^8. The tutorial walks through identifying U and U', applying the derivative formula, and performing substitutions to simplify the derivative to 96 * (4x - 7)^7.

What is the power rule of differentiation used for?

• Finding the integral of a function

• Determining the slope of a tangent line

• Calculating the derivative of a function raised to a power

• Solving differential equations

In the example function F(x) = 3 * (4x - 7)^8, what is the expression for U?

• 8x - 7

• 4x - 7

• 4x + 7

• 3x - 7

What is the derivative of U, or U prime, in the example function?

• 7

• 3

• 4

• 8

After applying the derivative formula, what is the simplified expression for the derivative of the example function?

• 96 * (4x - 7)^7

• 24 * (4x - 7)^8

• 96 * (4x - 7)^8

• 24 * (4x - 7)^7

Which rule is applied in conjunction with the power rule in this tutorial?

• Sum rule

• Chain rule

• Quotient rule

• Product rule