Right away I can see a glaring error:
You forgot that u is a function of x and y. This should beNeed help to check my working..
∂V/∂x = xf'(u) + f(u)
Your second derivative will also need adjusted accordingly.
Shortly thereafter, you substitute in as f'(u). This is simply wrong. f(u) is some unknown (arbitrary) function, and thus f'(u) is simply the derivative of that function, and cannot be substituted with anything else. (Try picturing the sample case . Then , which you can see is most definitely not