Question

y x2 + x y2 = 12 what is the derivative?

Answer 1

use implicit differentiation:
yx^2+xy^2=12
differentiate with respect to x (product rule):
(x^2y'+2xy) + (y^2+2xyy')=0
Solve for y':
y'=-(2xy+y^2)/(x^2+2xy)