Power Rule

AP Calculus · Axiom Academy

The most fundamental differentiation shortcut The Power Rule is the fastest way to find derivatives of polynomial functions. Instead of using the limit definition every time, we can use this simple formula: Let's apply the power rule to several functions: Using power rule (rewrite first!): The power rule works for all exponents, including negative and fractional ones: Step 4: Combining with Constants You'll often use the power rule together with the sum rule and constant multiple rule: This means you can differentiate each term of a polynomial separately: You've mastered the Power Rule! Next: The Product Rule—for multiplying functions.

This is the written version of the interactive lesson above. See the full AP Calculus course.