## Task Condition

Find the derivative.

$$
y=\frac{\sinh 3 x}{\sqrt{\cosh 6 x}}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\operatorname{sh} 3 x}{\sqrt{\operatorname{ch} 6 x}}\right)^{\prime}=\frac{3 \operatorname{ch} 3 x \cdot \sqrt{\operatorname{ch} 6 x}-\operatorname{sh} 3 x \cdot \frac{1}{2 \sqrt{\operatorname{ch} 6 x}} \cdot \operatorname{sh} 6 x \cdot 6}{\operatorname{ch} 6 x}= \\
& =\frac{3 \operatorname{ch} 3 x \cdot \operatorname{ch} 6 x-\operatorname{sh} 3 x \cdot \operatorname{sh} 6 x \cdot 3}{\operatorname{ch} 6 x \cdot \sqrt{\operatorname{ch} 6 x}}=\frac{3 \operatorname{ch} 3 x \cdot \operatorname{ch} 6 x-6 \operatorname{sh}^{2} 3 x \cdot \operatorname{ch} 3 x}{\operatorname{ch} 6 x \cdot \sqrt{\operatorname{ch} 6 x}}= \\
& =\frac{3 \operatorname{ch} 3 x \cdot\left(\operatorname{ch} 6 x-2 \operatorname{sh}^{2} 3 x\right)}{\operatorname{ch} 6 x \cdot \sqrt{\operatorname{ch} 6 x}}=\frac{3 \operatorname{ch} 3 x \cdot\left(1+2 \operatorname{sh}^{2} 3 x-2 \operatorname{sh}^{2} 3 x\right)}{\operatorname{ch} 6 x \cdot \sqrt{\operatorname{ch} 6 x}}= \\
& =\frac{3 \operatorname{ch} 3 x}{\operatorname{ch} 6 x \cdot \sqrt{\operatorname{ch} 6 x}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 11-14