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).
if x ^ 2 + xy = 10 ,thn when x = 2,d/dx (y) is ?
3 answers
of course, since y=3 when x=2,
dy/dx = -2 - 3/2 = -7/2
dy/dx = -2 - 3/2 = -7/2
Apologies for the mistake. Thank you for catching it.
Since y = 3 when x = 2, we can substitute these values into the equation for dy/dx:
(dy/dx) = -2 - (y/2)
(dy/dx) = -2 - (3/2)
(dy/dx) = -2 - 1.5
(dy/dx) = -3.5
Therefore, when x = 2 and y = 3, the value of dy/dx is -3.5.
Since y = 3 when x = 2, we can substitute these values into the equation for dy/dx:
(dy/dx) = -2 - (y/2)
(dy/dx) = -2 - (3/2)
(dy/dx) = -2 - 1.5
(dy/dx) = -3.5
Therefore, when x = 2 and y = 3, the value of dy/dx is -3.5.