## Task Condition

Find the derivative.

$y=\frac{1-8 \cosh^{2} x}{4 \cosh^{4} x}$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{1-8 \cosh^{2} x}{4 \cosh^{4} x}\right)^{\prime}=\frac{-16 \cosh x \cdot \sinh x \cdot \cosh^{4} x-\left(1-8 \cosh^{2} x\right) \cdot 4 \cosh^{3} x \cdot \sinh x}{4 \cosh^{8} x}= \\
& =\frac{-4 \cosh^{2} x \cdot \sinh x-\left(1-8 \cosh^{2} x\right) \cdot \sinh x}{\cosh^{5} x}=\frac{-4 \sinh x \cdot\left(\cosh^{2} x+1-2 \cosh^{2} x\right)}{\cosh^{5} x}= \\
& =\frac{4 \sinh^{3} x}{\cosh^{5} x}=\frac{4 \tanh^{3} x}{\cosh^{2} x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 11-22