AP Calculus AB/BC Formula Sheet
Every limit, derivative, and integral formula you need for the AP Calculus exam, verified against the latest College Board CED.
LIMITS & CONTINUITY
\lim_{x \to c} f(x) = LDefinition of a limitf(c) \text{ is defined, } \lim_{x \to c} f(x) \text{ exists, } \lim_{x \to c} f(x) = f(c)Definition of continuity\lim_{x \to 0} \frac{\sin x}{x} = 1Special trigonometric limitDERIVATIVES (RULES)
\frac{d}{dx}[f(g(x))] = f'(g(x))g'(x)Chain Rule\frac{d}{dx}[uv] = uv' + vu'Product Rule\frac{d}{dx}[\frac{u}{v}] = \frac{vu' - uv'}{v^2}Quotient RuleINTEGRALS
\int f(g(x))g'(x) dx = F(g(x)) + Cu-Substitution\int u dv = uv - \int v duIntegration by Parts\int_a^b f(x) dx = F(b) - F(a)FTC Part 2