\[1)Constant \space Rule:\frac{d}{dx}(c)=0\]
\[2)Constant \space Multiple\space Rule:\frac{d}{dx}(cf(x))=cf'(x)\]
\[3)Power \space Rule:\frac{d}{dx}(x^n)=nx^{n-1}\]
\[4)Sum \space Rule:\frac{d}{dx}[f(x)+g(x)]=f'(x)+g'(x)\]
\[5)Difference \space Rule:\frac{d}{dx}[f(x)-g(x)]=f'(x)-g'(x)\]
\[6)Product \space Rule:\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+g(x)f'(x)\]
\[7)Quotient \space Rule:\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}\]
\[8)Chain \space Rule:\frac{d}{dx}[f(g(x)]=f'(g(x))g'(x)\]
\[\frac{d}{dx}(e^x)=e^x\]
\[\frac{d}{dx}(a^x)=a^xln \space a\]
\[\frac{d}{dx}(e^{g(x)})=e^{g(x)}g'(x)\]
\[\frac{d}{dx}(a^{g(x)})=ln(a)a^{g(x)}g'(x)\]
\[\frac{d}{dx}(ln \space x)=\frac{1}{x}\]
\[\frac{d}{dx}(ln(g(x)))=\frac{g'(x)}{g(x)}\]
\[\frac{d}{dx}(log_{a}x)=\frac{1}{xlna}, \space x>0 \]
\[\frac{d}{dx}(log_{a}g(x))=\frac{g'(x)}{g(x)lna}\]
\[\frac{d}{dx}(sinx)=cosx\]
\[\frac{d}{dx}(cosx)=-sinx\]
\[\frac{d}{dx}(tanx)=sec^2x\]
\[\frac{d}{dx}(cosecx)=-cosecx \space cotx\]
\[\frac{d}{dx}(secx)=secx \space tanx\]
\[\frac{d}{dx}(cotx)=-cosec^2x\]
\[\frac{d}{dx}(sin^{-1}x)=\frac{1}{\sqrt{1+x^2}}\]
\[\frac{d}{dx}(cos^{-1}x)=\frac{-1}{\sqrt{1-x^2}}\]
\[\frac{d}{dx}(tan^{-1}x)=\frac{1}{\sqrt{1+x^2}}\]
\[\frac{d}{dx}(cot^{-1}x)=\frac{-1}{\sqrt{1+x^2}}\]
\[\frac{d}{dx}(sec^{-1}x)=\frac{1}{x\sqrt{x^2-1}}, \space x !=±1,0\]
\[\frac{d}{dx}(cosec^{-1}x)=\frac{-1}{x\sqrt{x^2-1}},\space x !=±1,0\]