Найти производную x-y+arcsin(xy)=0

Решите задачу:

$x-y+arcsin(xy)=0 \\ \\ y'= -\frac{F'_x}{F'_y} \\ \\ F_x'=1-0+ \frac{1}{ \sqrt{1-x^2} } \\ \\ F_y'=0-1+ \frac{1}{ \sqrt{1-y^2} }$

$y'= -\frac{1+ \frac{1}{ \sqrt{1-x^2} }}{-1+ \frac{1}{ \sqrt{1-y^2} }}=\frac{1+ \frac{1}{ \sqrt{1-x^2} }}{1- \frac{1}{ \sqrt{1-y^2} }}= \frac{ \frac{\sqrt{1-x^2}+1}{\sqrt{1-x^2}} }{ \frac{\sqrt{1-y^2}-1}{\sqrt{1-y^2}} } =\frac{\sqrt{1-x^2}+1}{\sqrt{1-x^2}}* \frac{\sqrt{1-y^2}}{\sqrt{1-y^2}-1} = \\ \\ =\frac{\sqrt{1-y^2}(\sqrt{1-x^2}+1)}{\sqrt{1-x^2}(\sqrt{1-y^2}-1)}$