Derivative of $$$\operatorname{atanh}{\left(x \right)}$$$
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Your Input
Find $$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right)$$$.
Solution
The derivative of the inverse hyperbolic tangent is $$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = \frac{1}{1 - x^{2}}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{1}{1 - x^{2}}\right)}$$Simplify:
$$\frac{1}{1 - x^{2}} = - \frac{1}{x^{2} - 1}$$Thus, $$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = - \frac{1}{x^{2} - 1}$$$.
Answer
$$$\frac{d}{dx} \left(\operatorname{atanh}{\left(x \right)}\right) = - \frac{1}{x^{2} - 1}$$$A
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