Найти производную: x^3y+x^2y^2+xy^3=0.

[latex]x^3y+x^2y^2+xy^3=0 \\\\ (x^3)'*y+x^3*y'+(x^2)'*y^2+x^2*(y^2)'+x'*y^3+x*(y^3)'=0 \\\\ 3x^2*y+x^3*y'+2x*y^2+x^2*2y*y'+1*y^3+x*3y^2*y'=0 \\\\ 3x^2y+x^3y'+2xy^2+2x^2yy'+y^3+3xy^2y'=0 \\\\ 3x^2y+2xy^2+y^3+(x^3+2x^2y+3xy^2)y'=0 \\\\ (x^3+2x^2y+3xy^2)y'=-3x^2y-2xy^2-y^3 \\\\ y'= \dfrac{-3x^2y-2xy^2-y^3}{x^3+2x^2y+3xy^2} [/latex]