Derivatives

$$f'(x) = {lim}↙{h→0}{ {f(x+h)-f(x)}/h}$$
$$d/{dx}(c)=0$$
$$d/{dx}(x^n)=nx^n-1$$
$$d/{dx}(cf(x)) = cf'(x)$$
$$d/{dx}(f(x)g(x)) = {f'(x)g(x)+f(x)g'(x)}$$
$$d/{dx}(f(x)±g(x)) = f'(x)±g'(x)$$
$$d/{dx}({f(x)}/{g(x)}) = {f'(x)g(x)-f(x)g'(x)}/{ {g(x)}^2}$$
$$d/{dx}(f(g(x))) = f'(g(x))g'(x)$$

USEFUL DERIVATIVES
$$d/{dx}(sin(x)) = cos(x)$$
$$d/{dx}(cos(x)) = -sin(x)$$
$$d/{dx}(tan(x)) = sec^2(x)$$
$$d/{dx}(sec(x)) = sec(x)tan(x)$$
$$d/{dx}(csc(x)) = -csc(x)cot(x)$$
$$d/{dx}(cot(x)) = -csc^2(x)$$
$$d/{dx}(sin^{-1}(x)) = 1/{√{1-x^2} }$$
$$d/{dx}(cos^{-1}(x)) = -1/{√{1-x^2} }$$
$$d/{dx}(tan^{-1}(x)) = 1/{ {1+x^2} }$$
$$d/{dx}(a^x) = a^{x}ln(a)$$
$$d/{dx}(e^x) = e^x$$
$$d/{dx}(ln(x)) = 1/x,x>0$$
$$d/{dx}(ln|x|) = 1/x,x≠0$$
$$d/{dx}(log_{a}(x)) = 1/{xln(a)},x>0$$