## Task Condition

Find the derivative.

$y=\ln \frac{x^{2}}{\sqrt{1-a x^{4}}}$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\ln \frac{x^{2}}{\sqrt{1-a x^{4}}}\right)^{\prime}=\frac{\sqrt{1-a x^{4}}}{x^{2}} \cdot\left(\frac{x^{2}}{\sqrt{1-a x^{4}}}\right)^{\prime} \\
& =\frac{\sqrt{1-a x^{4}}}{x^{2}} \cdot \frac{2 x \cdot \sqrt{1-a x^{4}}-x^{2} \cdot \frac{1}{2 \sqrt{1-a x^{4}}} \cdot\left(-4 a x^{3}\right)}{1-a x^{4}}= \\
& =\frac{1}{x} \cdot \frac{2 \cdot\left(1-a x^{4}\right)+2 a x^{4}}{1-a x^{4}}=\frac{2-2 a x^{4}+2 a x^{4}}{x\left(1-a x^{4}\right)}=\frac{2}{x-a x^{5}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 8-4