What is $\frac{d}{dx}\left(\cos^{-1}{\left(3 x \right)}\right)$ for $\lvert x \rvert < \frac{1}{3}$?

Explanation

1. 01

   $\frac{d}{dx}\cos^{-1} u = -\frac{u'}{\sqrt{1 - u^{2}}}$ with $u = 3x$.

2. 02

   $-\frac{3}{\sqrt{1 - 9x^{2}}}$.