The correct option (c) [{– 2xey – ex ∙ 2y(x + 1)}/{x(xey + ex ∙ 2)}]
Explanation:
x2 ey + 2xyex + 23 = 0
∴ differentiating wrt. x, we get
2xey + x2 ey (dy/dx) + 2[xyex + yex + xex (dy/dx)] + 0 = 0
∴ (dy/dx) [x2 ey + 2x ex] = – 2xey – 2xyex – 2yex
∴ (dy/dx) = [(– 2xey – 2xyex – 2yex)/(x2 ey + 2xex)]
∴ (dy/dx) = [{– 2xey – 2yex (x + 1)}/{x(xey + 2ex)}