Derivative

#Math

Types

Derivative List

$(f\pm g)'(x)=f'(x)\pm g'(x)$
$(f\cdot g)'=f'g+fg'$
$(\frac{f}{g})'=\frac{f'g-fg'}{g^2}$
$\frac{d}{dx}(f(g(x))=f'(g(x))\cdot g'(x)$
$(x^n)'=nx^{n-1}$
$(e^x)'=e^x$
$(\ln x)'=\frac{1}{x}$
$(\sin x)'=\cos x$
$(\cos x)'=-\sin x$
$(\tan x)'=\sec^2 x$
$(\csc x)' = -\csc x \cot x$
$(\sec x)' = \sec x \tan x$
$(\cot x)' = -\csc^2 x$
$(\sin^{-1}x)' = \frac{1}{\sqrt{1 - x^2}}$
$(\cos^{-1}x)' = -\frac{1}{\sqrt{1 - x^2}}$
$(\tan^{-1}x)'=\frac{1}{1+x^2}$
$(\csc^{-1}x)'=-\frac{1}{|x| \sqrt{x^2 - 1}}$
$\sec^{-1}x)' = \frac{1}{|x| \sqrt{x^2 - 1}}$
$(\cot^{-1}x)' = -\frac{1}{1+x^2}$
$(\sinh^{-1}x)' = \frac{1}{\sqrt{x^2 + 1}}, ~ x > 1$
$(\cosh^{-1}x)' = \frac{1}{\sqrt{x^2 - 1}}, ~ |x| < 1$
$(\tanh^{-1} x) = \frac{1}{1 - x^2}, ~ |x| < 1$
$(\text{csch}^{-1} ~ x)' = -\frac{1}{|x| \sqrt{1 + x^2}}, ~ x \ne 0$
$(\text{sech}^{-1} ~ x)' = -\frac{1}{x \sqrt{1 - x^2}}, ~ 0 < x < 1$
$(\coth^{-1} x)' = \frac{1}{1 - x^2}, ~ |x| > 1$