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 is A

\(\frac{\mathrm d}{\mathrm d x}(x^2 + xy - 5) = \frac{\mathrm d (x^{2})}{\mathrm d x} + \frac{\mathrm d (xy)}{\mathrm d x} - \frac{\mathrm d (5)}{\mathrm d x} = 0\)

= \(2x + x\frac{\mathrm d y}{\mathrm d x} + y = 0\)

\(\implies x\frac{\mathrm d y}{\mathrm d x} = -(2x + y)\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{-(2x + y)}{x}\)