Differentiation Table

\(\displaystyle\frac{d}{dx}a=0\)
\(\displaystyle\frac{d}{dx}x^a=ax^{a-1}\)
\(\displaystyle\frac{d}{dx}e^x=e^x\)
\(\displaystyle\frac{d}{dx}a^x=a^x\ln a\)
\(\displaystyle\frac{d}{dx}\ln x=\frac{1}{x}\)
\(\displaystyle\frac{d}{dx}\log_ax=\frac{1}{x\ln a}\)
\(\displaystyle\frac{d}{dx}\sin x=\cos x\)
\(\displaystyle\frac{d}{dx}\cos x=-\sin x\)
\(\displaystyle\frac{d}{dx}\tan x=\sec^2x\)
\(\displaystyle\frac{d}{dx}\cot x=-\csc^2x\)
\(\displaystyle\frac{d}{dx}\sec x=\tan x\sec x\)
\(\displaystyle\frac{d}{dx}\csc x=-\csc x\cot x\)
\(\displaystyle\frac{d}{dx}\sin^{-1}x=\frac{1}{\sqrt{1-x^2}}\)
\(\displaystyle\frac{d}{dx}\cos^{-1}x=\frac{-1}{\sqrt{1-x^2}}\)
\(\displaystyle\frac{d}{dx}\tan^{-1}x=\frac{1}{1+x^2}\)
\(\displaystyle\frac{d}{dx}\cot^{-1}x=\frac{-1}{1+x^2}\)
\(\displaystyle\frac{d}{dx}\sec^{-1}x=\frac{1}{\vert x\vert\sqrt{x^2-1}}\)
\(\displaystyle\frac{d}{dx}\csc^{-1}x=\frac{-1}{\vert x\vert\sqrt{x^2-1}}\)
\(\displaystyle\frac{d}{dx}(f(x)\pm g(x))=f'(x)\pm g'(x)\)
\(\displaystyle\frac{d}{dx}(af(x))=af'(x)\)
\(\displaystyle\frac{d}{dx}(f(x)g(x))=f'(x)g(x)+f(x)g'(x)\)
\(\displaystyle\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}\)
\(\displaystyle\frac{d}{dx}f^{-1}(x)=\frac{1}{f'\left(f^{-1}(x)\right)}\)
\(\displaystyle\frac{d}{dx}\left(\int_{g(x)}^{f(x)}h(s)\,ds\right)=h(f(x))f'(x)-h(g(x))g'(x)\)