## Task Condition

Find the derivative.

$y=x^{\sin x^{3}}$
## Solution

$y=x^{\sin x^{3}}$

$\ln y=\ln x^{\sin x^{3}}=\sin x^{3} \cdot \ln x$

$\frac{y^{\prime}}{y}=\cos x^{3} \cdot 3 x^{2} \cdot \ln x+\sin x^{3} \cdot \frac{1}{x}=3 x^{2} \cdot \ln x \cdot \cos x^{3}+\frac{\sin x^{3}}{x}$

$y^{\prime}=y \cdot\left(3 x^{2} \cdot \ln x \cdot \cos x^{3}+\frac{\sin x^{3}}{x}\right)=x^{\sin x^{3}} \cdot\left(3 x^{2} \cdot \ln x \cdot \cos x^{3}+\frac{\sin x^{3}}{x}\right)$

## Problem Kuznetsov Differentiation 12-14