In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent.

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反双曲函数是双曲函数的反函数。 记为（arsinh、arcosh、artanh等等）。 与 反三角函数 不同之处是它的前缀是ar意即area (面积)，而不是arc (弧)。 因为双曲角是以双曲线、通过原点直线以及其对x轴的映射三者之间所夹面积定义的，而圆角是以弧长与半径的比值定义。 [1] 我们知道， 三角函数 分为sin（正弦）、cos（余弦）、tan（正切）、cot（余切）、sec（正割）、csc（余割）六种。 而 双曲函数 也如此。 故而，反双曲函数也有六种。 有反双曲正弦、反双曲余弦、反双曲 …

6 days ago · The inverse hyperbolic sine (Beyer 1987, p. 181; Zwillinger 1995, p. 481), sometimes called the area hyperbolic sine (Harris and Stocker 1998, p. 264) is the multivalued function that is the inverse function of the hyperbolic sine.

求导范例： 设 θ = arsinh x，则： 使用 分部积分法 和上面的简单导数很容易得出它们。 ^ 双曲余弦函数是偶函数，所以对于一个y值（y>1），都有两个x值与之对应，取反的时候只取一个（通常是正的）即可。

该页面介绍了双曲函数与反双曲函数的一些公式。

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Nov 4, 2024 · Inverse hyperbolic functions are the inverse functions of the hyperbolic sine, cosine, tangent, and other hyperbolic functions. They are used to solve equations involving hyperbolic functions and are expressed in terms of logarithmic formulas. The …

Apr 26, 2023 · Let x ∈R x ∈ R be a real number. Let arsinh x arsinh x denote the inverse hyperbolic sine of x x. Then: For all x ∈ R x ∈ R we have that cosh y ≥ 1 cosh y ≥ 1. Thus it follows that it is necessary to take the positive root of sinh2 y + 1− −−−−−−−−√ sinh 2 y + 1. So: .

What is the first derivative of arcsinh (x) ?