Question: Consider the function \(f: \mathbb{R}^{2} \rightarrow \mathbb{R}\) given by

\[f(x, y)=\left\{\begin{array}{cl} \frac{x y}{\sqrt{x^{2}+y^{2}}}, & (x, y) \neq(0,0) \\ 0, & (x, y)=(0,0) \end{array}\right.\]

1. Is the point \((0,0)\) an interior point of the domain of \(f\) ?
2. If it is, determine from the definition the partial derivatives \(\partial f / \partial x(0,0)\) and \(\partial f / \partial y(0,0)\).
3. Find the directional derivative of \(f\) at \((0,0)\) in an arbitrary direction \(\mathbf{v}=\left(v_{1}, v_{2}\right)\).

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