Define \(f:\mathbb{R}^2\to\mathbb{R}\) by
\[
f(x,y)=
\begin{cases}
\dfrac{xy(x^2-y^2)}{x^2+y^2}, & (x,y)\ne(0,0),\\[6pt]
0, & (x,y)=(0,0).
\end{cases}
\]
Which statement about the mixed partial derivatives at \((0,0)\) is correct?
Select one option.
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