I think what you are reaching for is
though most would write this as
You can certainly take a partial derivative of a function y(x), but it is the same as an ordinary derivative.
Since y''' = 0 we know that y(x) = a + bx + (1/2)cx^2 where a, b, c are constants. We also know that y' = b + cx > 0 for all x. What does this say about b + cx?