基本求导公式

基本积分公式

• $(x^{\alpha })’=\alpha x^{\alpha -1}$
• $({\alpha }^x)’={\alpha }^x\ln \alpha (\alpha >0,\alpha \ne 1)$
• $(e^x)’=e^x$
• $({\log }_{\alpha }x)’=\frac{1}{x\ln \alpha }(\alpha >0,\alpha \ne 1)$

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• $(\ln |x|)’=\frac{1}{x}(x\ne 0)$
• $(\sin x)’=\cos x$
• $(\cos x)’=-\sin x$

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• $(\arcsin x{)}^{\prime }=\frac{1}{\sqrt{1-x^2}}$
• $(\arccos x)’=-\frac{1}{\sqrt{1-x^2}}$
• $(\tan x)’={\sec }^{2}x$
• $(\cot x)’=-{\csc }^{2}x$

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• $(\arctan x)’=\frac{1}{1+x^2}$
• $(\mathrm{arccot}x)’=-\frac{1}{1+x^2}$
• $(\sec x)’=\sec x\tan x$
• $(\csc x)’=-\csc x\cot x$

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• $[\ln (x+\sqrt{x^2+1})]’=\frac{1}{\sqrt{x^2+1}}$
• $[\ln (x+\sqrt{x^2-1})]’=\frac{1}{\sqrt{x^2-1}}$

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• $(\arctan \frac{1+x}{1-x}{)}^{\prime }=\frac{1}{1+x^2}$