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Calculus Formulas & Calculators

Understand calculus formulas with explanations, examples and interactive tools.

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\frac{d}{dx}x^n=nx^{n-1}

Differentiate a power of x.

\frac{d}{dx}\sin x=\cos x

Angles in radians.

\frac{d}{dx}\cos x=-\sin x

Angles in radians.

(fg)\prime=f\prime g+fg\prime

Differentiate product of two differentiable functions.

(f/g)\prime=\frac{gf\prime-fg\prime}{g^2}

Differentiate quotient when g ≠ 0.

\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}

Differentiate a composition of functions.

\int x^n dx=\frac{x^{n+1}}{n+1}+C

For n ≠ −1; indefinite integral.

\int\frac1x dx=\ln|x|+C

Antiderivative of 1/x for x ≠ 0.

\int_a^b f(x)dx=F(b)-F(a)

F is an antiderivative of continuous f.