## Task Condition

Find the derivative.

$y=-\frac{e^{3 x}}{3 \operatorname{sh}^{3} x}$
## Solution

$y^{\prime}=\left(-\frac{e^{3 x}}{3 \operatorname{sh}^{3} x}\right)^{\prime}=-\frac{3 e^{3 x} \cdot \operatorname{sh}^{3} x-e^{3 x} \cdot 3 \operatorname{sh}^{2} x \cdot \operatorname{ch} x}{3 \operatorname{sh}^{6} x}=$

$=-\frac{e^{3 x} \cdot \operatorname{sh} x-e^{3 x} \cdot \operatorname{ch} x}{\operatorname{sh}^{4} x}=\frac{e^{3 x} \cdot(\operatorname{ch} x-\operatorname{sh} x)}{\operatorname{sh}^{4} x}$

Kuznetsov Differentiation 7-28