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Revision:Differentiation of Hyperbolic Functions

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Differentiation of Hyperbolic Functions

Derivatives of Hyperbolic Functions

\dfrac{\text{d}}{\text{d} x}(\sinh x) = \cosh x


\dfrac{\text{d}}{\text{d} x}(\cosh x) = \sinh x


\dfrac{\text{d}}{\text{d} x}(\tanh x) = \mathrm{sech} ^2x


\dfrac{\text{d}}{\text{d} x}(\mathrm{sech} x) = -\mathrm{sech} x\tanh x


\dfrac{\text{d}}{\text{d} x}(\mathrm{cosech} x) = -\mathrm{cosech} x\coth x


\dfrac{\text{d}}{\text{d} x}(\coth x) = -\mathrm{cosech} ^2x


Derivatives of Inverse Hyperbolic Functions

\dfrac{\text{d}}{\text{d} x}(\mathrm{arsinh} x) = \dfrac{1}{\sqrt{x^2+1}}


\dfrac{\text{d}}{\text{d} x}(\mathrm{arcosh} x) = \dfrac{1}{\sqrt{x^2-1}}


\dfrac{\text{d}}{\text{d} x}(\mathrm{artanh} x) = \dfrac{1}{1-x^2}

Derivatives of Inverse Trigonometric Functions

\dfrac{\text{d}}{\text{d} x}(\arcsin x) = \dfrac{1}{\sqrt{1-x^2}}


\dfrac{\text{d}}{\text{d} x}(\arccos x) = \dfrac{-1}{\sqrt{1-x^2}}


\dfrac{\text{d}}{\text{d} x}(\arctan x) = \dfrac{1}{1+x^2}

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