## Problem Statement

Find the derivative.

$$
y=e^{\sin x}\left(x-\frac{1}{\cos x}\right)
$$
## Solution

$y^{\prime}=\left(e^{\sin x}\left(x-\frac{1}{\cos x}\right)\right)^{\prime}=\left(e^{\sin x}\right)^{\prime}\left(x-\frac{1}{\cos x}\right)+e^{\sin x}\left(x-\frac{1}{\cos x}\right)^{\prime}=$ $=e^{\sin x} \cdot \cos x \cdot\left(x-\frac{1}{\cos x}\right)+e^{\sin x}\left(1+\frac{1}{\cos ^{2} x} \cdot(-\sin x)\right)=$ $=e^{\sin x} \cdot\left(x \cdot \cos x-1+1-\frac{\sin x}{\cos ^{2} x}\right)=e^{\sin x} \cdot\left(x \cdot \cos x-\frac{\sin x}{\cos ^{2} x}\right)$

## Problem Kuznetsov Differentiation 7-24