List of differentiation identities

In differential calculus, this table lists derivatives of many functions. In the following, f and g are functions of x, and c is a constant with respect to x.

${d \over dx}f(g(x))={d \over dg}f(g(x)){d \over dx}g(x)$

${d \over dx}c=0$

${d \over dx}x=1$

${d \over dx}cf(x)=c{d \over dx}f(x)$

${d \over dx}x^{c}=cx^{c-1}$

${d \over dx}(f(x)+g(x))={d \over dx}f(x)+{d \over dx}g(x)$

${d \over dx}f(x)g(x)={d \over dx}f(x)\cdot g(x)+f(x)\cdot {d \over dx}g(x)$

${d \over dx}{f(x) \over g(x)}={{d \over dx}f(x)\cdot g(x)-f(x)\cdot {d \over dx}g(x) \over (g(x))^{2}}$

${d \over dx}|x|={x \over |x|}$

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

${d \over dx}c^{x}={c^{x}\ln c}$

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

${d \over dx}\ln |x|={1 \over x}$

${d \over dx}\log _{c}x={1 \over x\ln c},\qquad c\geq 0$

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

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

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

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

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

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