## Problem Statement

Find the derivative.





Translate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.
## Solution

$$
\begin{aligned}
& y^{\prime}=-\frac{1}{2} \cdot \frac{(\operatorname{sh} x)^{\prime} \operatorname{ch}^{2} x-\operatorname{sh} x\left(\operatorname{ch}^{2} x\right)^{\prime}}{\operatorname{ch}^{4} x}+\frac{(\operatorname{sh} x)^{\prime}}{\operatorname{sh}^{2} x}-\frac{3}{2} \cdot \frac{(\operatorname{sh} x)^{\prime}}{1+\operatorname{sh}^{2} x}= \\
& =-\frac{1}{2} \cdot \frac{\operatorname{ch}^{3} x-2 \operatorname{sh} x \operatorname{ch} x \cdot \operatorname{sh} x}{\operatorname{ch}^{4} x}+\frac{\operatorname{ch} x}{\operatorname{sh}^{2} x}-\frac{3}{2} \cdot \frac{\operatorname{ch} x}{\operatorname{ch}^{2} x}=-\frac{\operatorname{ch} x\left(\operatorname{ch}^{2} x-2 \operatorname{sh}^{2} x\right)}{2 \operatorname{ch}^{4} x}+\frac{\operatorname{ch} x}{\operatorname{sh}^{2} x}-\frac{3}{2} \cdot \frac{\operatorname{ch} x}{\operatorname{ch}^{2} x}= \\
& =\frac{\operatorname{ch} x}{\operatorname{sh}^{2} x}+\frac{2 \operatorname{sh}^{2} x-\operatorname{ch}^{2} x-3 \operatorname{ch}^{2} x}{2 \operatorname{ch}^{3} x}=\frac{\operatorname{ch} x}{\operatorname{sh}^{2} x}+\frac{\operatorname{sh}^{2} x-2 \operatorname{ch}^{2} x}{\operatorname{ch}^{3} x}=\frac{\operatorname{ch} x}{\operatorname{sh}^{2} x}-\frac{2-\operatorname{sh}^{2} x}{\operatorname{ch}^{3} x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 11-27