Answer:
((4xysqrt(xy))-y)/(x-2x^2sqrt(xy))
Step-by-step explanation:
Treat y as a function of x and use the chain rule.
Use the chain rule and product rule:
(y+xy')/2sqrt(xy) = d/dx[8+x^2y]
(y+xy')/2sqrt(xy) = d/dx[x^2y]
Use product rule
(y+xy')/2sqrt(xy) = 2xy + x^2y'
Now solve for y'
y+xy' = (2xy)(2sqrt(xy))+ (x^2y')(2sqrt(xy))
xy'-2x^2y'sqrt(xy) = (2xy)(2sqrt(xy))-y
y'(x-2x^2sqrt(xy))
y' = ((4xysqrt(xy))-y)/(x-2x^2sqrt(xy))
