2018年9月19日 · Problem Prove formula $\\operatorname{arctanh} x = \\frac{1}{2} \\ln \\left(\\frac{1+x}{1-x}\\right)$ Attempt to solve To start off with definition of functions ...

The two functions resemble each other on the real line, but they're not the only sigmoidal functions around. . There are functions as simple as $\dfrac{x}{\sqrt{1+x^2}}$ and as complicated as $\dfrac2{\sqrt \pi}\int_0^x e^{-t^2}\mathrm dt$ that also have the s-s

2016年8月25日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2019年4月12日 · Just for some background knowledge, I am doing this because I am trying to show that the derivative of arctanh(x) = $\frac{1}{1-x^2}$ How do I prove that the integral below is equal to arctanh(x)?

2023年7月11日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2023年12月26日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2017年11月10日 · $\DeclareMathOperator{\th}{th}\DeclareMathOperator{\sh}{sh}\DeclareMathOperator{\ch}{ch}$ Let's set $\begin{cases} a=\arcsin(\th(x))\in[-\frac{\pi}2,\frac{\pi}2 ...

2016年6月13日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.