Find the $dz/dx$ in implicit function

Question

Maybe it's a stupid question, but if someone could look at this exercise in order to clarify my thoughts. It's from the basics of multivariable calculus: Let $f(x, y, z) = x-2xyz$ where $z = z(x,y)$. The task is to find partial derivatives of $\frac{dz}{dx}$ and $\frac{\partial z}{\partial x}$. The question is: Is it a mistake in this exercise or $\frac{dz}{dx}$ differs from $\frac{\partial z}{\partial x}$? If it does, then how do I compute the result of $\frac{dz}{dx}$? I do know how to do the former one but latter - no clue. Thanks in advance