If (y^{2} + xy – x = 0), find (frac{mathrm d y}{mathrm d x}).
-
A.
(frac{1 – y}{2y}) -
B.
(frac{1 – 2y}{x}) -
C.
(frac{1 – y}{x + 2y}) -
D.
(frac{1}{x + 2y})
Correct Answer: Option C
Explanation
Given (y^{2} + xy – x = 0)
Using the method of implicit differentiation, we have
(2yfrac{mathrm d y}{mathrm d x} + xfrac{mathrm d y}{mathrm d x} + y – 1 = 0)
(frac{mathrm d y}{mathrm d x}(2y + x) = 1 – y)
(frac{mathrm d y}{mathrm d x} = frac{1 – y}{x + 2y})