Differential

TARGET DECK Mathematics::Differential

$\sinh x$::$\cosh x$

$\cosh x$::$\sinh x$

$\tanh x$::${\mathrm{sech}}^{2}x$

$\coth x$::$-{\mathrm{csch}}^{2}x$

$\mathrm{sech}x$::$-\mathrm{sech}x\tanh x$

$\mathrm{csch}x$::$-\mathrm{csch}x\coth x$

${\sin }^{-1}x$::$\frac{1}{\sqrt{1-x^2}}(-1<x<1)$

${\cos }^{-1}x$::$-\frac{1}{\sqrt{1-x^2}}(-1<x<1)$

${\tan }^{-1}x$::$\frac{1}{1+x^2}(-\infty <x<\infty )$

${\csc }^{-1}x$::$-\frac{1}{|x|\sqrt{x^2-1}}(|x|>1)$

${\sec }^{-1}x$::$\frac{1}{|x|\sqrt{x^2-1}}(|x|>1)$

${\cot }^{-1}x$::$-\frac{1}{1+x^2}(-\infty <x<\infty )$

${\sinh }^{-1}x$::$\frac{1}{\sqrt{x^2+1}}$

${\cosh }^{-1}x$::$\frac{1}{\sqrt{x^2-1}}u>1$

${\tanh }^{-1}x$::$\frac{1}{1-x^2}|u|<1$

${\coth }^{-1}x$::$\frac{1}{1-x^2}|u|>1$

${\mathrm{sech}}^{-1}x$::$-\frac{1}{|x|\sqrt{1-x^2}}0<u<1$

${\mathrm{csch}}^{-1}x$::$-\frac{1}{|x|\sqrt{1+x^2}}u\ne 0$