Derivative Formulas

d/dx\left(c\right)

0

d/dx\left(x\right)

1

d/dx\left(cx\right)

c

d/dx\left(x^{n}\right)

nx^{n-1}

d/dx\left(e^{x}\right)

e^{x}

d/dx\left(\ln x\right)

\frac{1}{x}

d/dx\left(a^{x}\right)

a^{x}\cdot\ln a

d/dx\left(\log_{a}x\right)

\frac{1}{x}\cdot\frac{1}{\ln a}

d/dx\left(\sin x\right)

\cos x

d/dx\left(\cos x\right)

-\sin x

d/dx\left(\tan x\right)

\sec^2x

d/dx\left(\cot x\right)

-\csc^2x

d/dx\left(\sec x\right)

\sec x\tan x

d/dx\left(\csc x\right)

-\csc x\cot x

d/dx\left(\arcsin x\right)

\frac{1}{\sqrt{1-x^2}}

d/dx\left(\arccos x\right)

-\frac{1}{\sqrt{1-x^2}}

d/dx\left(\arctan x\right)

\frac{1}{1+x^2}

d/dx\left(arc\cot x\right)

-\frac{1}{1+x^2}

d/dx\left(\operatorname{arcsec}x\right)

\frac{1}{\left|x\right|\sqrt{x^2-1}}

d/dx (\operatorname{arccsc}x)

-\frac{1}{\left|x\right|\sqrt{x^2-1}}