Problem $1.$ Use implicit differentiation to find $d\frac{y}{d}x$ if

$($a$)y^2=x^2+2x$

$($e$)x+tanxy=0$

$($b$)2\sqrt[\phantom{2}]{y}=x-y$

$($f$)x^4+siny=x^3{y}^2$

$($c$)y^2-2x=1-2y$

$($g$)x^3+y^2=si{n}^{2}y$

$($d$)xy+y^2=1$

$($h$)x{y}^3+x^{2}y=6$