Hyperbolic derivatives
Derivatives of sinh, cosh and tanh.
Derivative of sinh x
\frac{d}{dx}\,\sinh x = \cosh x
The derivative of sinh x is cosh x. See the proof from the exponential definition, why there is no minus sign, chain rule examples and a graph.
Derivative of cosh x
\frac{d}{dx}\,\cosh x = \sinh x
The derivative of cosh x is sinh x, with no minus sign. See the proof from exponentials, the hanging cable example, chain rule examples and a graph.
Derivative of tanh x
\frac{d}{dx}\,\tanh x = \operatorname{sech}^2 x
The derivative of tanh x is sech² x, which equals 1 − tanh² x. See the quotient rule proof, chain rule examples, a graph and the arctanh derivative.
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