## Problem Statement

Find the derivative.

$$
y=\frac{\operatorname{sh} x}{1+\operatorname{ch} x}
$$
## Solution

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

## Problem Kuznetsov Differentiation 11-12