Suppose we have the following function: $$f(x,y) = \sqrt{|xy|}$$ Is this function differentiable at $(0,0)$? Are the partial derivatives continuous at $(0,0)$?
The answer says it is differentiable but the partials are not continuous at that point
2026-04-09 02:03:15.1775700195
Differentiability of multi-variable function
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Hint for the differentiable question: If $f$ were differentiable at $(0,0),$ then as a function of $x,$ $f(x,x) = |x|$ would be differentiable at $0.$ Is this true?