(e) Prove that the function \( f(x, y)=\sqrt{|x y|} \) is not differentiable at \( (0,0) \), but both \( f_{x} \) and \( f_{y} \) exist at origin.
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The function is \( f(x, y) = \sqrt{|xy|} \). At the origin, \( f(0, 0) = \sqrt{|0 \cdot 0|} = 0 \). Show more…
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