Ask a Math Geek: differentiate

July 20, 2011

The Power Rule

This is a calculus lesson based on a question:

Would you be able to explain how to derive a square root?

The power rule is used to find the derivative of (or "differentiate" or "find the instantaneous rate of change of") an algebraic expression of the form x to a numerical power, or xⁿ.

The derivative of a function ƒ(x) = xⁿ is ƒ'(x) = n * x^n-1. If it is easier to remember think of it as dragging the exponent down (to multiply the x by) and then subtracting one in the exponent.

Here are some examples to clarify:

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Qualifications

The Math Geek (that's me) is a student in her junior (third) year of college. She graduated with an Associate's Degree (and a 4.0 GPA) in Adolescent Mathematics Education and is two years away from obtaining a Bachelor's Degree and Teacher Certification in New York State. Her mathematics background involves Algebra, Trigonometry, and Geometry (ages 13-15); Precalculus (ages 15-16); Single-Variable Calculus (ages 16-18); Multi-Variable Calculus, Differential Equations, Proofs, Discrete Math, Linear Algebra, Statistics, and Physics (ages 18-20).
She has been tutoring for pay for two years, as well as volunteering for countless years previous. Most of the students she tutors are at the pre-algebra, algebra, or pre-calculus level.