Derivative/Formulas

List of formulas

$\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)$

$(f(x)+g(x))' = f'(x) + g'(x)$

$\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}$

$(f(g(x)))' = f'(g(x))g'(x)$

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

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

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

$\frac d{dx} \tan x = \sec^2 x$

$\frac d{dx} \sec x = \sec x \tan x$

$\frac d{dx} \csc x = -\csc x\cot x$

$\frac d{dx} \cot x = -\csc^2 x$

$\frac d{dx} e^x = e^x$

$\frac d{dx} a^x = (\log_e a) a^x

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

$\frac d{dx} \arcsin x = \frac 1{\sqrt{1-x^2}}$

$\frac d{dx} \arccos x = -\frac 1{\sqrt{1-x^2}}$

$\frac d{dx} \arctan x = \frac 1{1+x^2}$

$\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\mid x \mid\sqrt{x^2-1}}$

$\frac d{dx} arccsc x = - \frac 1{x\sqrt{x^2 - 1}}$

$\frac d{dx} \arccot x = - \frac 1{1+x^2}$

See also

• Calculus
• Derivative