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f\left(x\right)=e^{x}
f^{\prime}\left(x\right)=e^{x}
f\left(x\right)=\ln x
f^{\prime}\left(x\right)=\frac{1}{x}
f\left(x\right)=\sin x
f^{\prime}\left(x\right)=\cos x
f\left(x\right)=\cos x
f^{\prime}\left(x\right)=-\sin x
f\left(x\right)=\tan x
f^{\prime}\left(x\right)=\sec^2x
f\left(x\right)=\cot x
f^{\prime}\left(x\right)=-\csc^2x
f\left(x\right)=\sec x
f^{\prime}\left(x\right)=\sec x\tan x
f\left(x\right)=\csc x
f^{\prime}\left(x\right)=-\csc x\cot x