Differentiate (x^{2} + xy – 5 = 0).
-
A.
(frac{-(2x + y)}{x}) -
B.
(frac{(2x – y)}{x}) -
C.
(frac{-x}{2x + y}) -
D.
(frac{(2x + y)}{x})
Correct Answer: Option A
Explanation
(frac{mathrm d}{mathrm d x}(x^2 + xy – 5) = frac{mathrm d (x^{2})}{mathrm d x} + frac{mathrm d (xy)}{mathrm d x} – frac{mathrm d (5)}{mathrm d x} = 0)
= (2x + xfrac{mathrm d y}{mathrm d x} + y = 0)
(implies xfrac{mathrm d y}{mathrm d x} = -(2x + y))
(frac{mathrm d y}{mathrm d x} = frac{-(2x + y)}{x})