Understanding the Power Rule in Calculus

Nancy introduces the power rule, a shortcut for finding derivatives, and demonstrates its application on polynomials. She explains how to handle terms with constants, negative powers, and fractional powers using the power rule, constant multiple rule, and sum and difference rule. The video concludes with a discussion on the implications of using these rules for different types of powers.

What is the main advantage of using the power rule over the formal limit definition of derivatives?

• It provides a deeper understanding.

• It is faster and less tedious.

• It is applicable to all functions.

• It is more accurate.

When applying the power rule to the term x^4, what is the resulting derivative?

• 4x^3

• x^3

• 4x^4

• x^4

How do you handle a constant when using the power rule on a term like 2x^3?

• Add the constant to the derivative.

• Subtract the constant from the derivative.

• Multiply the constant by the derivative of the power.

• Ignore the constant.

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

• 0

• x

• 1

• x^2

What is the derivative of a constant term, such as -1?

• -1

• 0

• It depends on the context.

• 1

What rule allows you to differentiate each term of a polynomial separately?

• Quotient Rule

• Sum and Difference Rule

• Chain Rule

• Product Rule

Which rule states that the derivative of a constant is zero?

• Power Rule

• Constant Rule

• Quotient Rule

• Product Rule

How do you handle a negative power when using the power rule?

• Leave the power unchanged.

• Add 1 to the power.

• Multiply the power by -1.

• Subtract 1 from the power.

What must you do when subtracting 1 from a fractional power?

• Add 1 instead.

• Convert the fraction to a decimal.

• Find a common denominator.

• Multiply by the reciprocal.

What happens to the derivative of a fractional power less than 1 at x = 0?

• It becomes infinite.

• It equals one.

• It equals zero.

• It becomes undefined.