Derivatives Rules of Hyperbolic functions

There are six derivative rules to evaluate the differentiation of the hyperbolic functions in differential calculus. So, learn every derivative formula of hyperbolic functions with mathematical proofs.

Hyperbolic sine function

$\dfrac{d}{dx}{\,\sinh{x}} \,=\, \cosh{x}$

Hyperbolic Cosine function

$\dfrac{d}{dx}{\,\cosh{x}} \,=\, \sinh{x}$

Hyperbolic Tan function

$\dfrac{d}{dx}{\,\tanh{x}} \,=\, \operatorname{sech}^2{x}$

Hyperbolic Cot function

$\dfrac{d}{dx}{\,\coth{x}} \,=\, -\operatorname{csch}^2{x}$

Hyperbolic Secant function

$\dfrac{d}{dx}{\,\operatorname{sech}{x}} \,=\, -\operatorname{sech}{x}\tanh{x}$

Hyperbolic Cosecant function

$\dfrac{d}{dx}{\,\operatorname{csch}{x}} \,=\, -\operatorname{csch}{x}\coth{x}$