## Task Condition

Find the derivative.

$y=\frac{\sqrt{x-1}(3 x+2)}{4 x^{2}}$
Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\sqrt{x-1}(3 x+2)}{4 x^{2}}\right)^{\prime}=\frac{\left(\frac{1}{2 \sqrt{x-1}} \cdot(3 x+2)+\sqrt{x-1} \cdot 3\right) \cdot x^{2}-\sqrt{x-1}(3 x+2) \cdot 2 x}{4 x^{4}}= \\
& =\frac{((3 x+2)+6(x-1)) \cdot x-4 \cdot(x-1)(3 x+2)}{8 x^{3} \sqrt{x-1}}= \\
& =\frac{(9 x-4) \cdot x-4 \cdot\left(3 x^{2}+2 x-3 x-2\right)}{8 x^{3} \sqrt{x-1}}=\frac{9 x^{2}-4 x-12 x^{2}+4 x+8}{8 x^{3} \sqrt{x-1}}= \\
& =\frac{-3 x^{2}+8}{8 x^{3} \sqrt{x-1}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 6-14