I was watching one of the Khan Academy videos on differential equations ("Exact Equations Intuition 1 (proofy)") and there's something that confused me.
In the video, they use both the derivative of a function $\psi(x, y(x))$ with respect to $x$,
$\frac{d}{dx}\psi(x, y(x)),$
as well as the partial derivative of the same function with respect to the same variable,
$\frac{\partial \psi}{\partial x}$
(I think) I understand what a partial derivative of a function is (you consider its other arguments constants and you essentially turn it into a derivative of a single variable function), but I don't understand what a non-partial derivative with respect to one variable means. How is it different from a partial derivative?