Answer
$-7$
Work Step by Step
Since, we have $\dfrac{\partial w}{\partial v}=\dfrac{\partial w}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial w}{\partial y}\dfrac{\partial y}{\partial v}$
or, $=(2x-\dfrac{y}{x^2})(-2)+(\dfrac{1}{x})(1)$
or, $=(2(u-2v+1)-\dfrac{(2u+v-2)}{(u-2v+1)^2})(-2)+(\dfrac{1}{(u-2v+1)})$
Now, at point $u=0,v=0$, we get
$\dfrac{\partial w}{\partial v}=(2(0-0+1)-\dfrac{(0+0-2)}{(0-0+1)^2})(-2)+(\dfrac{1}{(0-0+1)})=-7$
