Is it possible to take the derivative of multiple variables in a single derivative rather than in multiple partial derivatives? For example: $$\frac{\delta}{\delta (xy)} (x^2y)$$
My first thought is to change variables such that $w = xy$, resulting in
$$\frac{\delta}{\delta w}(wx)$$ but $w$ is still dependent on $x$, which shows up in the differentiating term.
Is what I'm thinking unnecessary in math or is there something to this?
