$${D(F) = (\frac{\partial F}{\partial x} \mid_{x,y,z,...})^2 D(x) + (\frac{\partial F}{\partial y} \mid_{x,y,z,...})^2 D(y) + (\frac{\partial F}{\partial z} \mid_{x,y,z,...})^2 D(z) + ...}$$