Answer
$b \dfrac{\partial w}{\partial x}=a \dfrac{\partial w}{\partial y} $
Work Step by Step
Since, $\dfrac{\partial u}{\partial y}=b$ and $\dfrac{\partial u}{\partial x}=a$
Now, $\dfrac{\partial w}{\partial x}=\dfrac{\partial w}{\partial u} \ \dfrac{\partial u}{\partial x}=a \dfrac{\partial w}{\partial u}...(1)$
and $\dfrac{\partial w}{\partial y}=\dfrac{\partial w}{\partial u} \ \dfrac{\partial u}{\partial y}=b \dfrac{\partial w}{\partial u}...(2)$
Equation (1) and (2) can be written as: $\dfrac{1}{a} \dfrac{\partial w}{\partial x}=\dfrac{\partial w}{\partial u}$ and $\dfrac{1}{b} \dfrac{\partial w}{\partial y}=\dfrac{\partial w}{\partial u}$
This implies that $\dfrac{1}{a} \dfrac{\partial w}{\partial x}=\dfrac{1}{b} \dfrac{\partial w}{\partial y}$
Therefore, $b \dfrac{\partial w}{\partial x}=a \dfrac{\partial w}{\partial y} $
