d$)$ Given that e $^$ x $+$ xy $+$ ln$(1+2$x$)=1$ where x $>=0$

Show that $($e$\text{'}+$ x$)*($d $^2*$ y$)/($d $*$ x $^2)+$ e$\text{'}*($d$/$dx $($y$))^2+2*$ d$/$dx $($y$)-4/((1+2$x$)^2)=0$

ii$.$ Hence, find d the value of d$/$dx $($y$)$ the point $(0,0).$