Question

f(x) = (archtanh √3x^2)^3

Answer 1

$\displaystyle f(x) = (\mathrm{archtanh}(\sqrt{3x^2}))^3\\ \begin{aligned} f'(x) &= 3(\mathrm{archtanh}(\sqrt{3}x))^2 \times \sqrt{3} \times \frac{1}{1 - 3x^2} \\&= \frac{3\sqrt{3}(\mathrm{arctanh}(\sqrt{3x^2}))^2}{1 - 3x^2} \end{aligned}$