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Derivative formulas

The following is a list of functions and their derivatives:

f(x)=a \rightarrow f'(x)=0

f(x)=x^n \rightarrow f'(x)=nx^{n-1}

f(x)=a^x \rightarrow f'(x)=a^x \ln a

f(x)=e^x \rightarrow f'(x)=\frac{1}{x\ln a}

f(x)=\ln x \rightarrow f'(x)=\frac{1}{x}

The following is a list of trigonometric functions and their derivatives:

f(x)=\sin x \rightarrow f'(x)=\cos x

f(x)=\cos x \rightarrow f'(x)=-\sin x

f(x)=\tan x \rightarrow f'(x)=\frac{1}{cos^2 x}

f(x)=\cot x \rightarrow f'(x)=-\frac{1}{sin^2 x}

f(x)=\arcsin x \rightarrow f'(x)=\frac{1}{\sqrt{1-x^2}}

f(x)=\arccos x \rightarrow f'(x)=-\frac{1}{\sqrt{1-x^2}}

f(x)=\arctan x \rightarrow f'(x)=\frac{1}{1+x^2}

f(x)=\text{arccot} x \rightarrow f'(x)=-\frac{1}{1+x^2}

You can also use these results in derivative calculations:

f(x)=\frac{1}{x} \rightarrow f'(x)=-\frac{1}{x^2}

f(x)=\sqrt{x} \rightarrow f'(x)=\frac{1}{2\sqrt{x}}

Tip: Usually you will be required to derive functions that are composed of elementary functions. Therefore, it is advisable to make sure that you know the Derivative Rules well in order to avoid common mistakes.

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