HallsFor a general function of two variables, that is wrong. The definition of "differential" of a function of one variable is \(\displaystyle df= \frac{df}{dx}dx\). But for a function of two variables, x and t, \(\displaystyle df= \frac{\partial f}{\partial x}dx+ \frac{\partial f}{\partial t}dt\).
Was this function, f, assumed to have any special properties?
Ew! Not good even for a Physics book. Unless it's supposed to be something like \(\displaystyle df = \dfrac{\partial f}{\partial x^i} dx^i\) and we're using the Einstein convention.Halls
Viona is reading some book in physics that seems to be more than a bit casual in its use of mathematical notation. She really needs to give more context for us to be of any assistance.