Question

is dy/dx f(x) the exact equivalent to the partial derivative of f(x) w.r.t. x?

Answer 1

Ummmm y...e..ss.. I think so.

Since f is only a function of 1 variable (x), it's the same as taking the normal derivative of f WRT x.

It would be a different story if we were taking the partial of f(x,y) WRT x, since there is something going on with the other variable.
But since we have f(x), When we take the partial, ALL variables are accounted for.

Hopefully that makes sense D:

Answer 2

That makes sense. Thank you for the clear and concise answer =)