Question

Find dy/dx by implicit differentiation.

x^5(x + y) = y^2(9x − y)

this is what i've got so far but I don't think it is the right answer.

y'= 9y^2-6x^5-5x^3y/x^5+9y^2-18xy

Answer 1

x^5(x + y) = y^2(9x − y)
5x^4(x+y) + x^5(1+y') = 2yy'(9x-y) + y^2(9-y')

5x^5+5x^4y + x^5 + x^5y' = 18xyy' - 2y^2y' + 9y^2 + y^2y'

y'(x^5 - 18xy - 3y^2) = 9y^2 -6x^5 - 5x^4y

y' = (9y^2-6x^5-5x^4y)/(x^5-18xy-3y^2)

you were close, but must have messed up some signs somewhere.