## Problem Statement

Find the derivative.

$$
y=3 \frac{\sin x}{\cos ^{2} x}+2 \frac{\sin x}{\cos ^{4} x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=3 \frac{\cos ^{3} x-\sin x \cdot 2 \cos x \cdot(-\sin x)}{\cos ^{4} x}+2 \frac{\cos ^{5} x-\sin x \cdot 4 \cos ^{3} x \cdot(-\sin x)}{\cos ^{8} x}= \\
& =3 \frac{\cos ^{2} x+2 \sin ^{2} x}{\cos ^{3} x}+2 \frac{\cos ^{2} x+4 \sin ^{2} x}{\cos ^{5} x}=3 \frac{1-\sin ^{2} x+2 \sin ^{2} x}{\cos ^{3} x}+2 \frac{1-\sin ^{2} x+4 \sin ^{2} x}{\cos ^{5} x}= \\
& =\frac{3+3 \sin ^{2} x}{\cos ^{3} x}+\frac{2-6 \sin ^{2} x}{\cos ^{5} x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 15-5