$$$\operatorname{atanh}{\left(x \right)}$$$的导数

该计算器将求$$$\operatorname{atanh}{\left(x \right)}$$$的导数，并显示步骤。

求$$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right)$$$。

反双曲正切函数的导数为 $$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = \frac{1}{1 - x^{2}}$$$：

$${\color{red}\left(\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{1}{1 - x^{2}}\right)}$$

化简：

$$\frac{1}{1 - x^{2}} = - \frac{1}{x^{2} - 1}$$

因此，$$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = - \frac{1}{x^{2} - 1}$$$。

$$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = - \frac{1}{x^{2} - 1}$$$A

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