## Problem Statement

Find the derivative.

$$
y=\arcsin \frac{x-2}{(x-1) \sqrt{2}}
$$
Solution

$y^{\prime}=\left(\arcsin \frac{x-2}{(x-1) \sqrt{2}}\right)^{\prime}=\frac{1}{\sqrt{1-\left(\frac{x-2}{(x-1) \sqrt{2}}\right)^{2}}} \cdot\left(\frac{x-2}{(x-1) \sqrt{2}}\right)^{\prime}=$

$$
\begin{aligned}
& =\frac{(x-1) \sqrt{2}}{\sqrt{\left.(x-1)^{2} \cdot 2-(x-2)\right)^{2}}} \cdot \frac{1}{\sqrt{2}} \cdot \frac{1 \cdot(x-1)-(x-2) \cdot 1}{(x-1)^{2}}= \\
& =\frac{1}{\sqrt{2 x^{2}-4 x+2-\left(x^{2}-4 x+4\right)}} \cdot \frac{1}{x-1}=\frac{1}{\sqrt{x^{2}-2}} \cdot \frac{1}{x-1}= \\
& =\frac{1}{(x-1) \sqrt{x^{2}-2}}
\end{aligned}
$$

Problem Kuznetsov Differentiation 10-22