I know the proof of the statement "If partial derivatives exist in a n-ball $B(\vec{a})$ and are continuous at $\vec{a}$, then the function is differentiable at $\vec{a}$ " . But I was wondering whether the converse holds.
I was thinking along these lines that, differentiability at a point implies the existence of tangent plane, and that $\vec{a}$ lies on that plane. This would mean that the partial derivatives do exist, but I'm not able to visualize or proceed any further.