Warning

This document was AI generated.

The equation $ax^n$ is the standard form used for differentiating terms in a polynomial.

The Power Rule

To differentiate $ax^n$, you multiply the coefficient ($a$) by the power ($n$) and then subtract 1 from the power.

$f(x) = ax^n \implies f'(x) = anx^{n-1}$

Examples

• $y = x^3 \implies \frac{dy}{dx} = 3x^2$
• $y = 5x^4 \implies \frac{dy}{dx} = 20x^3$
• $y = 10 \implies \frac{dy}{dx} = 0$

Common Transformations

Before differentiating, terms must be in the $ax^n$ format.

Differentiation Table