# Derivative/Formulas

## List of formulas

 $\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)$ $(f(x)+g(x))' = f'(x) + g'(x)$ $\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}$ $(f(g(x)))' = f'(g(x))g'(x)$ $\frac d{dx} x^n = n x^{n-1}$ $\frac d{dx} \sin x = \cos x$ $\frac d{dx} \cos x = -\sin x$ $\frac d{dx} \tan x = \sec^2 x$ $\frac d{dx} \sec x = \sec x \tan x$ $\frac d{dx} \csc x = -\csc x\cot x$ $\frac d{dx} \cot x = -\csc^2 x$ $\frac d{dx} e^x = e^x$ $\frac d{dx} a^x = (\ln a) a^x$ $\frac d{dx} \ln x = \frac 1x$ $\frac d{dx} \log_b x =\frac{\log_b e}{x}$ $\frac d{dx} \arcsin x = \frac 1{\sqrt{1-x^2}}$ $\frac d{dx} \arccos x = -\frac 1{\sqrt{1-x^2}}$ $\frac d{dx} \arctan x = \frac 1{1+x^2}$ $\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\mid x \mid\sqrt{x^2-1}}$ $\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}$ $\frac d{dx} \arccot x = - \frac 1{1+x^2}$ (Error compiling LaTeX. ! Undefined control sequence.)