I am talking about the theroem stated in : Mathematical Analysis, by Tom Apostol page $357$.
$\textbf{Theorem.}$ Assume that one of the partial derivatives $D_{1}\mathbf{f},\cdots D_{n}\mathbf{f}$ exists at $\mathbf{c}$ and that the remaining $n-1$ partial derivatives exists in some $n$-ball $B(\mathbf{c})$, and are continuous at $\mathbf{c}$. Then $f$ is differentiable at $\mathbf{c}$.
Although I have searched extensively, I am not able to find an example of this theorem.Can anyone please post example(s) of this theorem here? I looked through the following pages here (and more):
Equivalent condition for differentiability on partial derivatives
Partial derivatives of $f$ exist, but only $n-1$ of them are continuous, implies differentiability
Continuity of one partial derivative implies differentiability
