Show that for a gradient system $\bf\dot x= f(x)$, $\frac{\partial f_i}{\partial x_j}-\frac{\partial f_j}{\partial x_i}=0$ for $1 \leq i, j \leq d$
$\frac{\partial f_i}{x_j}=\frac{\partial f_j}{x_i}\implies(f_1,\ldots,f_n)$ is a gradient