I'm reading a book where the symbol $D$ is used for vector differentiation. The problem is, I can't find out if $D_x$ is the total derivative or the partial derivative. Specifically, in the following formula:
$$D_xf(x,y(x))$$ I can interpret this in two ways $$\begin{align} &1. \quad D_xf(x,z)|_{z=y(x)}& \\ &2. \quad D_xg(x)&\text { where } g(x)=f(x,y(x)) \end{align}$$
Which of these two interpretations is correct? Is there a generally accepted convention for that? Also, where does $\nabla$ fit in? i.e. is there a generally accepted interpretation of the respective meanings of the following two expressions? $$\begin{align}\nabla_xf(x,y(x))\\ D_xf(x,y(x)) \end{align}$$