## moderately complicated derivatives

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 $$x \in (-\infty, 0) \cup (0, \infty)$$,
• $$f(0) = 0$$.