Is nabla/del defined for $\nabla{V(x(t),t)}$?

Question

I stumbled upon this article, where they write $\nabla V(x(t), t)$. But, because $x$ is a function of $t$, isn't we suppose to use the ordinary derivative of $V$ instead? I mean isn't the following wrong: $$ \nabla V(x(t),t)=\Bigg( \frac{\partial V(x(t),t)}{\partial x},\frac{\partial V(x(t),t)}{\partial y},\frac{\partial V(x(t),t)}{\partial z}\Bigg) \quad ? $$ I'm not interested in the equation in the article, just the notation $∇V(x(t), t)$.