To find the derivative of y with respect to x, we can differentiate the equation x^2 + xy = 10 with respect to x using the product rule and chain rule.
Differentiating both sides with respect to x:
2x + x(dy/dx) + y = 0
Rearranging the equation and isolating dy/dx:
x(dy/dx) = -2x - y
(dy/dx) = (-2x - y) / x
Substituting x = 2 into the equation for dy/dx:
(dy/dx) = (-2(2) - y) / 2
(dy/dx) = (-4 - y) / 2
(dy/dx) = -2 - (y/2)
Therefore, when x = 2, d/dx (y) is -2 - (y/2).