Let's say I have a function $f = f(x,y)$ and a differential equation where partial derivative appears, for example $\frac{\partial f}{\partial x}$. I also have a substitution $t$, which contains both $x$ and $y$ variables, so, I guess, it's $t(x,y)$. How can I use this substitution to get derivative of an one-variable function, $\frac{df}{dx}$?
I understand, what I should do in a case with two substitutions: $t=t(x,y)$ and $p=p(x,y)$, I'd use a rule $\frac{\partial f}{\partial x}=\frac{\partial f}{\partial t}\frac{\partial t}{\partial x}+\frac{\partial f}{\partial p}\frac{\partial p}{\partial x}$. But I'd still get a partial derivative and I don't have second substitution function.