The Power Rule

Derivatives without limits

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Power rule: $\frac{d}{dx}x^n = n x^{n-1}$, for any power $n$.
• Constant multiples carry through, sums split term by term, and constants have derivative 0.
• The tangent at $x = a$ is $y = f(a) + f'(a)(x - a)$.

Steps

1. Pattern
2. The power rule
3. Practice
4. Term by term
5. Negative powers
6. Square roots
7. Find the steep spot
8. Tangent line