## Task Condition

Find the derivative.

$y=x^{\arcsin x}$
## Solution

$y=x^{\arcsin x}$

$\ln y=\arcsin x \cdot \ln x$

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

$=\frac{\ln x}{\sqrt{1-x^{2}}}+\frac{\arcsin x}{x}$

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

## Problem Kuznetsov Differentiation 12-6