## Condition of the problem

Find the derivative.

$$
y=\frac{1+8 \operatorname{ch}^{2} x \cdot \ln (\operatorname{ch} x)}{2 \operatorname{ch}^{2} x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{1+8 \cosh^{2} x \cdot \ln (\cosh x)}{2 \cosh^{2} x}\right)^{\prime}=\left(\frac{1}{2 \cosh^{2} x}+4 \ln (\cosh x)\right)^{\prime}= \\
& =-2 \cdot \frac{1}{2 \cosh^{3} x} \cdot \sinh x+4 \cdot \frac{1}{\cosh x} \cdot \sinh x=-\frac{\sinh x}{\cosh^{3} x}+\frac{4 \sinh x}{\cosh x}= \\
& =\frac{4 \sinh x \cdot \cosh^{2} x-\sinh x}{\cosh^{3} x}=\frac{\sinh x \cdot\left(4 \cosh^{2} x-1\right)}{\cosh^{3} x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 11-15