CalculusDerivatives

Derivative Rules cheat sheet

11 calculus formulas on one page. Print it or save it as a PDF from the print dialog.

Constant

\frac{d}{dx}c = 0

Power

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

Product

(fg)' = f'g + fg'

Quotient

\left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}

Chain

\left(f(g(x))\right)' = f'(g(x))\,g'(x)

Exponential

\frac{d}{dx}a^x = a^x \ln a

Logarithm

\frac{d}{dx}\ln x = \frac{1}{x}

Sine and cosine

(\sin x)' = \cos x,\ (\cos x)' = -\sin x

Tangent

(\tan x)' = \sec^2 x

Inverse sine

(\arcsin x)' = \frac{1}{\sqrt{1 - x^2}}

Inverse tangent

(\arctan x)' = \frac{1}{1 + x^2}

Put the formulas to work