Derivatives of Hyperbolic Functions

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Theorem

This page gathers together derivatives of hyperbolic functions.


Let $u$ be a differentiable real function of $x$.


Derivative of Hyperbolic Sine Function

$\map {\dfrac \d {\d x} } {\sinh u} = \cosh u \dfrac {\d u} {\d x}$


Derivative of Hyperbolic Cosine Function

$\map {\dfrac \d {\d x} } {\cosh u} = \sinh u \dfrac {\d u} {\d x}$


Derivative of Hyperbolic Tangent Function

$\map {\dfrac \d {\d x} } {\tanh u} = \sech^2 u \dfrac {\d u} {\d x}$


Derivative of Hyperbolic Cotangent Function

$\map {\dfrac \d {\d x} } {\coth u} = -\csch^2 u \dfrac {\d u} {\d x}$


Derivative of Hyperbolic Secant Function

$\map {\dfrac \d {\d x} } {\sech u} = -\sech u \tanh u \dfrac {\d u} {\d x}$


Derivative of Hyperbolic Cosecant Function

$\map {\dfrac \d {\d x} } {\csch u} = -\csch u \coth u \dfrac {\d u} {\d x}$