I need to find dy/dx of this function and evaluate the derivative at the point (2,-1)
x^2 y+y^2 x = -2 solve the equation to be = 0
x^2y + y^2x +2 = 0 find partial derivatives for dy and dx,
the first term has two parts
x^2y has two partial derivatives 2xy dx + x^2 dy
the second term has 2 parts
y^2x has 2 partial derivatives y^2 dx + 2yx dy
and 2 has no derivative
2xy dx + y^2 dx + x^2 dy + 2yx dy = 0
2xy + y^2 dx = (-x^2 - 2xy) dy
dy/dx = (2xy + y^2)/(-x^2 - 2xy)
use the point (2,-1)
dy/dx = [2*2*(-1) + (-1)^2]/[-1(2)^2 -2*2*(-1)]
dy/dx = (-4 + 1) / (-4 + 4) there is a 0 in the de=nominator therefore it is undefined