Common Derivatives

**Common Derivatives**
Function	Derivative w.r.t. $x$	Example
$\text{Constant}\,$	$0\,$	$y=4,\qquad \frac{dy}{dx}=0\,$
$x^n\,$	$nx^{n-1}\,$	$y=x^7,\qquad \frac{dy}{dx}=7x^6\,$
$e^x\,$	$e^x\,$	$y=e^x,\qquad \frac{dy}{dx}=e^x\,$
$\sin {(x+b)}\,$	$a\cdot \cos {(ax+b)}\,$	$y=\sin{(3x+4)},\qquad \frac{dy}{dx}=3\cdot \cos{(3x+4)}\,$
$cos(ax+b)\,$	$-a\cdot sin(ax+b)\,$	$y=cos(3x+4), dy/dx=-3\cdot sin(3x+4)$
$tan(ax+b)\,$	$a\cdot sec^2(ax+b)\,$	$y=tan(3x+4), \frac{dy}{dx}=3\cdot sec^2(3x+4)$
$s e c (a x + b)$	$a\cdot sec(ax+b)\cdot tan(ax+b)$	$y=sec(5x-4), dy/dx=5\cdot sec(5x-4)\cdot tan(5x-4)$
$c o s e c (a x + b)$	$-a\cdot cosec(ax+b)\cdot cot(ax+b)$	$y=cosec(5x-4), dy/dx=-5\cdot cosec(5x-4)\cdot cot(5x-4)$
$c o t (a x + b)$	$-a\cdot cosec^2(ax+b)$	$y=cot(3x+4), dy/dx=-3\cdot cosec^2(3x+4)$
$l o g (a x + b)$	$a/(ax+b)\,$	$y=log(3x+4), dy/dx=3/(3x+4)\,$
$a / g (x)$	$- a g'(x) / (g (x)) 2$	$y=1/(x^2+1), dy/dx=-2x/(x^2+1)^2\,$