Derivative Rules

You can find any derivative from the limit definition — but it's slow algebra every time. Calculus offers a better way: a small set of rules that deliver derivatives in one line. The power rule alone handles every polynomial. The product and quotient rules handle multiplication and division. And the chain rule — the deepest of them all — handles functions inside functions, the composition you met in pre-calculus. With these four, you can differentiate essentially any function you'll encounter, turning a tedious limit into a mechanical pattern.