A similar notation is Lagrange notation, which is really useful for studying derivatives as a member of a larger class of operators.
The derivative w.r.t. x of f(x) is D_x f in Lagrange notation. It looks a bit like matrix multiplication for a good reason—a matrix is just a representation of a linear operator on a finite dimensional vector space.
The derivative w.r.t. x of f(x) is D_x f in Lagrange notation. It looks a bit like matrix multiplication for a good reason—a matrix is just a representation of a linear operator on a finite dimensional vector space.