In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

Hyperbolic tangent "tanh" (pronounced "than"): tanh(x) = sinh(x) cosh(x) = e x − e-x e x + e-x. tanh vs tan . Hyperbolic cotangent: coth(x) = cosh(x) sinh(x) = e x + e-x e x − e-x . Hyperbolic secant: sech(x) = 1 cosh(x) = 2 e x + e-x . Hyperbolic cosecant "csch" or "cosech": csch(x) = 1 sinh(x) = 2 e x − e-x. Why the Word "Hyperbolic" ?

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In this short lesson, you will learn about Tanh hyperbolic function and its properties including tanh function, tanh calculator, tanh formula, and tanh equation. You can see the graphical representation of the Tanh function in the image below.

$\tanh \frac{x}{2} = \pm \sqrt{\frac{\cosh x - 1}{\cosh x + 1}}$ [+ if x > 0, - if x . 0] $=\frac{\text{sinh}(x)}{1 + \text{cosh}(x)} = \frac{\text{cosh}(x) - 1}{\text{sinh}(x)}$ Multiple angle formulas $\sinh 3x = 3 \sinh x + 4 \sinh^3 x$ $\cosh 3x = 4 \cosh^3 x - 3 \cosh x$ $\tanh 3x = \frac{3 \tanh x + \tanh^3 x}{1 + 3 \tanh^2x}$

This tanh calculator is the ultimate tool you need to deal with the hyperbolic tangent function! In what follows, we will explain what tanh is in math and how to calculate both the inverse and the derivative of tanh. We won't forget to give you extra tips on how to use this hyperbolic tangent calculator most efficiently. Let's go!

TANH (x) returns the hyperbolic tangent of the angle x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function.

Illustrated definition of Tanh: The Hyperbolic Tangent Function. tanh (x) (esupxsup minus esupminusxsup) (esupxsup esupminusxsup)...

Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. Tanh [ α ] is defined as the ratio of the corresponding hyperbolic sine and hyperbolic cosine functions via .

Jun 25, 2024 · 在众多激活函数中，双曲正切函数（Hyperbolic Tangent Function，简称 (\tanh)）是一个经典的选择，特别是在早期的深度学习模型中。 在浅层网络和特定任务中具有明显的优势，但在深层网络中，由于梯度消失问题，ReLU、Leaky ReLU 和 Swish 等激活 函数 表现更 …