Yeah, I was working through this problem and it differs from the answer that my friend got.(adsbygoogle = window.adsbygoogle || []).push({});

Using implicit differentiation, find the derivative of [tex]\mbox{arc}\tanh \frac{x}{2}[/tex] and state the domain for which the derivative applies

[tex]\begin{align*}

y = \arctanh \frac{x}{2} \\

\Leftrightarrow x = 2 \tanh y

\end{align*}[/tex]

[tex]\frac{d}{dx}x = \frac{d}{dx}2 \tanh y[/tex]

[tex]\Rightarrow 1 = 2\ \mbox{sech}^2 y \cdot \frac{dy}{dx}[/tex]

[tex]\Rightarrow \frac{dy}{dx} = \frac{1}{2\ \mbox{sech}^2 y}[/tex]

[tex]\Rightarrow \frac{dy}{dx} = \frac{1}{2 - 2 \tanh^2 y}[/tex]

[tex]\Rightarrow \frac{dy}{dx} = \frac{1}{2 - 2 \frac{x^2}{4}}[/tex]

[tex]\Rightarrow \frac{dy}{dx} = \frac{1}{2 - \frac{x^2}{2}}[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Derivative of arctanh

**Physics Forums | Science Articles, Homework Help, Discussion**