The Power Rule

Business Calculus · Axiom Academy

The most fundamental shortcut for finding derivatives Using the limit definition of the derivative is powerful but tedious. Let's discover a shortcut by looking at some derivatives we've already computed: The exponent comes down as a coefficient, and the new exponent is one less than before! If n is any real number, then: "Bring down the power, reduce by one" This rule works for any real exponent: positive, negative, fractions, even irrational numbers! Let's practice applying the power rule to different functions: Example 3: f(x) = x (same as x^1 ) The derivative of x is always 1 . This makes sense: y = x is a line with slope 1! The power rule works for any real exponent. First, let's rewrite some common functions using exponents: Example: Find the derivative of f(x) = Example: Find the derivative of f(x) = x^2 Click each problem to reveal the answer. Try to solve it yourself first! What is the derivative of f(x) = x^ -1/2 ? You've mastered the Power Rule! Remember: This rule is the foundation for most derivative calculations. Next, we'll learn how to combine it with other rules.

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