Hyperbolic functions

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Trigonometric functions
Hyperbolic functions
Logarithm
Conics
Vector

Derivative
Integral
Series
Ordinary differential equation

Definition

$$\begin{array}{l} \sinh x = \frac{e^x - e^{-x}}{2} \\ \cosh x = \frac{e^x + e^{-x}}{2} \end{array}$$

Identities

$$\begin{array}{ll} \sinh 0 = 0 & \sinh(-x) = -\sinh x \\ \cosh 0 = 1 & \cosh(-x) = \cosh x \\ \cosh x > \sinh x & \lim_{x \rightarrow \pm \infty} \tanh x = \pm 1 \end{array}$$
$$\begin{array}{l} \cosh^2 x - \sinh^2 x = 1 \\[12pt] \sinh(x + y) = \sinh x \cosh y + \cosh x \sinh y \\ \cosh(x + y) = \cosh x \cosh y + \sinh x \sinh y \\[12pt] \cosh x + \sinh x = e^{x} \\ \cosh x - \sinh x = e^{-x} \end{array}$$