Correct Answer: Option C

Explanation

Given \(y^{2} + xy - x = 0\)

Using the method of implicit differentiation, we have

\(2y\frac{\mathrm d y}{\mathrm d x} + x\frac{\mathrm d y}{\mathrm d x} + y - 1 = 0\)

\(\frac{\mathrm d y}{\mathrm d x}(2y + x) = 1 - y\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{1 - y}{x + 2y}\)

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