I've no clue how to get started .I'am unable to even understand what the hint is saying.I need your help please.
Given $$u = f(ax^2 + 2hxy + by^2), \qquad v = \phi (ax^2 + 2hxy + by^2),$$ then prove that
$$\frac{\partial }{\partial y} \left ( u\frac{\partial u }{\partial x} \right ) = \frac{\partial }{\partial x}\left ( u \frac{\partial v}{\partial y} \right ).$$
Hint. Given $$u = f(z),v = \phi(z), \text{where} z = ax^2 + 2hxy + by^2$$