Differentiate \(x^{2} + xy - 5 = 0\).
Question 1 Report
Differentiate \(x^{2} + xy - 5 = 0\).
Answer Details
To differentiate the equation, we need to find the derivative of each term in it, using the rules of differentiation.
\begin{align*}
\frac{d}{dx}(x^{2} + xy - 5) &= \frac{d}{dx}(0) \\
\frac{d}{dx}(x^{2}) + \frac{d}{dx}(xy) - \frac{d}{dx}(5) &= 0 \\
2x + y\frac{dx}{dx} + x\frac{dy}{dx} - 0 &= 0 \\
2x + y + x\frac{dy}{dx} &= 0 \\
x\frac{dy}{dx} &= -(2x + y) \\
\frac{dy}{dx} &= -\frac{2x+y}{x}
\end{align*}
Therefore, the correct answer is \(\frac{-(2x + y)}{x}\).
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