Derivatives Using Power (Exponent) Rule

The video tutorial introduces the power rule, a method for differentiating polynomials. It explains what polynomials are, provides examples of polynomials and non-polynomials, and demonstrates how to apply the power rule to differentiate functions. The tutorial also includes computational steps for finding derivatives using the power rule.

What is the primary purpose of the power rule in differentiation?

• To find the limit of a function

• To solve algebraic equations

• To differentiate polynomial functions

• To integrate polynomial functions

Which of the following is an example of a polynomial?

• ln(X) + X^4

• e^X + X^2

• sin(X) + X^3

• X^2 + 3

Why can't the power rule be used to differentiate X^5 * cos(X)?

• Because it involves a trigonometric function

• Because it is a polynomial

• Because it is a constant function

• Because it is a linear function

Which of the following functions can be differentiated using the power rule?

• 3X^2 + 4X^5

• e^X * X^2

• X^3 * ln(X)

• X^4 * sin(X)

What is the first step in applying the power rule to differentiate Y = 3X^4?

• Subtract one from the exponent

• Multiply the exponent by the constant

• Add one to the exponent

• Divide the exponent by the constant

In the function Y = CX^N, what does 'C' represent?

• The constant

• The variable

• The derivative

• The exponent

After applying the power rule to Y = 2X^3, what is the new exponent of X?

• 4

• 1

• 2

• 3