Answer
$\dfrac{1+2y}{1-2y}$
Work Step by Step
Differentiate $x$ and $y$ with respect to $u$.
$1=2x \times x_u-2yy_u .....(a) \\ 0=2x \times x_u -y_u ....(b)$
Now, multiply equation (b) by $2y$ and subtract from equation $a$. Solving for $x_u$ gives:
$x_u= \dfrac{1}{2x-4xy}$
Subtract equation $(b)$ from equation $a$.
$2x x_u -2y y_u -(2xx_u-y_u)=1-0 \implies y_u = 2x\dfrac{1}{1-2y}$
Now, differentiate $s$ with respect to $u$.
$s_u=2xx_u +2yy_u =2x \times ( \dfrac{1}{2x-4xy}) +2y \times (\dfrac{1}{1-2y})$
So, $s_u=\dfrac{1}{1-2y}+\dfrac{2y}{1-2y}=\dfrac{1+2y}{1-2y}$
