The diagonal derivative of a skew Schur polynomial

We prove a formula for the image of a skew Schur polynomial $s_{\lambda \mathrm{/}\mu }(x_1,x_2,\dots ,x_N)$ under the differential operator $\mathrm{\nabla }:={\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }{x}_1}}+{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }{x}_2}}+\cdots +{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }{x}_N}}$. This generalizes a formula of Weigandt for $\mathrm{\nabla }\left(s_{\lambda }\right)$.