## Task Condition

Find the derivative.

$y=\frac{\sqrt{2 x+3}(x-2)}{x^{2}}$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\sqrt{2 x+3}(x-2)}{x^{2}}\right)^{\prime}=\frac{\left(\frac{1}{2 \sqrt{2 x+3}} \cdot 2 \cdot(x-2)+\sqrt{2 x+3}\right) x^{2}-\sqrt{2 x+3}(x-2) \cdot 2 x}{x^{4}}= \\
& =\frac{((x-2)+(2 x+3)) x-(2 x+3)(x-2) \cdot 2}{x^{3} \sqrt{2 x+3}}= \\
& =\frac{(3 x+1) x-2\left(2 x^{2}+3 x-4 x-6\right)}{x^{3} \sqrt{2 x+3}}= \\
& =\frac{3 x^{2}+x-4 x^{2}+2 x+12}{x^{3} \sqrt{2 x+3}}=\frac{-x^{2}+3 x+12}{x^{3} \sqrt{2 x+3}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 6-17