常用求导公式

2020-11-02 本文已影响0人出题老头

${(x^a)}' = ax^{a-1}$
${(a^x)}' = a^x \ln a$
${(e^x)}' = e^x$
${(\ln x)}' = \frac{1}{x}$
${(\sin x)}' = \cos x$
${(\cos x)}' = -\sin x$
${( \tan x)}' = \sec^2 x$
${(\sec x)}' = \sec x \tan x$
${(\cot x)}' = - \csc^2 x$
${(\csc x)}' = - \csc x \cot x$
${(\arcsin x)}' = \frac{1}{ \sqrt {1-x^2}}$
${(\arccos x)}' = - \frac{1}{ \sqrt {1-x^2}}$
${(\arctan x )}' = \frac{1}{ 1+x^2}$
${( \textrm{arccot} x)}' = - \frac {1}{1+x^2}$
${(\ln (x+ \sqrt {x^2+1}))}' = \frac{1}{ \sqrt {1+x^2}}$
${(\ln (x+ \sqrt {x^2-1}))}' = \frac{1}{ \sqrt {x^2 - 1}}$

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