Condition of the problem

Find the derivative.

$y=2 \sqrt{x}-4 \ln (2+\sqrt{x})$
## Solution

$$
\begin{aligned}
& y^{\prime}=(2 \sqrt{x}-4 \ln (2+\sqrt{x}))^{\prime}=2 \cdot \frac{1}{2 \sqrt{x}}-4 \cdot \frac{1}{2+\sqrt{x}} \cdot \frac{1}{2 \sqrt{x}}= \\
& =\frac{2+\sqrt{x}}{\sqrt{x}(2+\sqrt{x})}-\frac{2}{(2+\sqrt{x}) \sqrt{x}}=\frac{\sqrt{x}}{\sqrt{x}(2+\sqrt{x})}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 8-3