Solve frac{frac{-1-y_{0}}{1/2-x_{0}}--1}{frac{|x_{0}-y_{0}+1|}{sqrt{2}}-frac{5sqrt{2}}{4}}

$$\frac { \frac { - 1 - y _ { 0 } } { \frac { 1 } { 2 } - x _ { 0 } } - - 1 } { \frac { | x _ { 0 } - y _ { 0 } + 1 | } { \sqrt { 2 } } - \frac { 5 \sqrt { 2 } } { 4 } }$$

Evaluate

$$-\frac{2\sqrt{2}\left(2x_{0}+2y_{0}+1\right)}{\left(1-2x_{0}\right)\left(2|x_{0}-y_{0}+1|-5\right)}$$

Differentiate w.r.t. x_0

$$\frac{4\sqrt{2}\left(-4x_{0}y_{0}sign(x_{0}-y_{0}+1)-4sign(x_{0}-y_{0}+1)x_{0}^{2}+2y_{0}sign(x_{0}-y_{0}+1)-4y_{0}|x_{0}-y_{0}+1|+sign(x_{0}-y_{0}+1)-4|x_{0}-y_{0}+1|+10y_{0}+10\right)}{\left(\left(1-2x_{0}\right)\left(2|x_{0}-y_{0}+1|-5\right)\right)^{2}}$$