## moderately complicated derivatives

### Task number: 3016

Determine the derivatives of the following functions at points where the derivative exists:

#### Variant 1

\[ \frac{2^x - 1}{3x}. \]

#### Variant 2

\[\hbox{arctan} (\ln x).\]

#### Variant 3

\[\arcsin(\sin x)) \]

#### Variant 4

The function \(f\) is defined by the rules:

- \(f(x) = x^2 \sin \left(\frac{1}{x}\right)\) for \(x \in (-\infty, 0) \cup (0, \infty)\),
- \(f(0) = 0\).