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