Three examples for how to use the power rule

The video tutorial explains the power rule for derivatives, demonstrating how to apply it to different types of expressions, including those with fractions, negative exponents, and roots. The instructor provides examples and clarifies common misconceptions, ensuring students understand how to rewrite expressions to apply the power rule effectively.

What is the first step in applying the power rule to differentiate an expression like x^n?

• Add 1 to the exponent

• Multiply the exponent by x

• Divide the exponent by x

• Bring the exponent down and subtract 1

When dealing with a fraction in the power rule, what should you do with the exponent in the denominator?

• Add 1 to the exponent

• Convert it to a positive exponent

• Leave it as is

• Move it to the numerator and make it negative

How should you present your final answer when using the power rule with negative exponents?

• In any form

• With the exponent doubled

• As a positive exponent

• As a negative exponent

What is the equivalent of a root in terms of exponents?

• A doubled exponent

• An exponent of zero

• A fractional exponent

• A negative exponent

When converting a root to a rational exponent, what should you ensure about the exponent?

• It should be doubled

• It should be zero

• It should be negative

• It should be positive