## Task Condition

Find the derivative.

$$
y=\frac{2\left(\sqrt{2^{x}-1}-\operatorname{arctg} \sqrt{2^{x}-1}\right)}{\ln 2}
$$
## Solution

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

## Problem Kuznetsov Differentiation 7-9