If 3y^2 - 2xy - x = 0 , then the value of dy dx at y = 2 is...

Step-by-step solution

Given equation is 3y^2 - 2xy - x = 0 . Substituting y = 2 in the equation: 3(2)^2 - 2x(2) - x = 0 12 - 4x - x = 0 5x = 12 x = 12 5 Differentiating the given equation with respect to x : d dx (3y^2 - 2xy - x) = 0 6y dy dx - 2 (y + x dy dx ) - 1 = 0 (6y - 2x) dy dx = 2y + 1 dy dx = 2y + 1 6y - 2x Substituting x = 12 5 and y = 2 : dy dx = 2(2) + 1 6(2) - 2 ( 12 5 ) dy dx = 5 12 - 24 5 dy dx = 5 36 5 = 25 36 Answer: 25 36