Derivatives

$$\frac{d}{dx}C=0,whereC=constat$$

$$\frac{d}{dx}{x}^n=n{x}^{n-1}$$

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

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

$$\frac{d}{dx}{\sin }^{-1}x=\frac{1}{\sqrt{1-x^2}}$$

$$\frac{d}{dx}{\cos }^{-1}x=-\frac{1}{\sqrt{1-x^2}}$$

$$\frac{d}{dx}{a}^x=a^x\ln a$$

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

$$\frac{d}{dx}\sinh x=\cosh x$$

$$\frac{d}{dx}\cosh x=\sinh x$$

$$\frac{d}{dx}{\sinh }^{-1}x=\frac{1}{\sqrt{x^2+1}}$$

$$\frac{d}{dx}{\cosh }^{-1}x=\frac{1}{\sqrt{x^2-1}}$$

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

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

$$\frac{d}{dx}{\tan }^{-1}x=\frac{1}{1+x^2}$$

$$\frac{d}{dx}{\cot }^{-1}x=\frac{-1}{1+x^2}$$

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

$$\frac{d}{dx}\tanh x=\frac{1}{{\cosh }^{2}x}$$

$$\frac{d}{dx}\coth x=\frac{1}{{\sinh }^{2}x}$$

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

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

$$\frac{d}{dx}{\sec }^{-1}x=\frac{1}{x\sqrt{x^2-1}}$$

$$\frac{d}{dx}{\csc }^{-1}x=\frac{-1}{x\sqrt{x^2-1}}$$

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