## Problem Statement

Find the derivative.

$$
y=(\tan x)^{\ln (\tan x) / 4}
$$
## Solution

$$
\begin{aligned}
& y=(\tan x)^{\ln (\tan x) / 4} \\
& \ln y=\frac{\ln (\tan x)}{4} \cdot \ln (\tan x) \\
& \ln y=\frac{\ln ^{2}(\tan x)}{4} \\
& \frac{y^{\prime}}{y}=\left(\frac{\ln ^{2}(\tan x)}{4}\right)^{\prime}=\frac{2 \ln (\tan x)}{4} \cdot \frac{1}{\tan x} \cdot \frac{1}{\cos ^{2} x}=\frac{\ln (\tan x)}{2 \sin x \cdot \cos x}= \\
& =\frac{\ln (\tan x)}{\sin 2 x} \\
& y^{\prime}=y \cdot \frac{\ln (\tan x)}{\sin 2 x}=(\tan x)^{(\ln (\tan x) / 4)} \cdot \frac{\ln (\tan x)}{\sin 2 x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 12-26