If \(x^2+2xy+y^3=10\), then value of \(\displaystyle\frac{dy}{dx}\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{-2(x+y)}{2x+3y^2}\)
Differentiating implicitly with respect to x (product rule for 2xy):
\( \displaystyle 2x + 2y + 2x\,\frac{dy}{dx} + 3y^2\,\frac{dy}{dx} = 0 \)
\( \displaystyle (2x+3y^2)\,\frac{dy}{dx} = -2(x+y) \)
\( \displaystyle \frac{dy}{dx} = \frac{-2(x+y)}{2x+3y^2} \)