Answer by Mittens for Can a function have partial derivatives, be continuous...
To complement user's answer, I would like to point out that the example in the OP is even more striking since not only do partial derivatives $\partial_1f(0,0)$ and $\partial_2f(0,0)$ exists, but also...
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By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.The existence...
View ArticleCan a function have partial derivatives, be continuous but not be...
I have a function:$$ f(x,y)= \begin{cases} \dfrac{2x^2y+y^3}{x^2+y^2} & \text{if $(x,y) \neq (0,0)$}\\ 0 & \text{if $(x,y) = (0,0)$}\\ \end{cases}$$which I think I managed to show:a) continuity...
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