You're totally right... but the previous poster is too. I encounter many students who really freak out at f(t) = y vs f(t) = x vs f(x) = y. Obviously they don't understand very well. I go back and forth between using notation as a crutch (always stay consistent so we can focus on the topic instead of the notation) and trying to really wean students from notation-dependence (let's do f(smily face) = y today! let's rotate all the axes and draw this with the z-axis sticking out!).

When people have very fragile understanding, they may be genuinely unsure if derivative with respect to x is computed the same way as derivative with respect to n. After all, x is always a real-valued variable and n is always a non-negative integer.... right?