Find \( \frac{d y}{d x}\left(x^{2} y^{2}+x y\right)=1 \)

1.	Find \( \frac{d y}{d x}\left(x^{2} y^{2}+x y\right)=1 \)
Answer» x²y³ + xy = 1 Differentiating both sides w.r.t. x 3 x²y²\(\frac{dy}{dx}+2xy^3+x\frac{dy}{dx}+y=0\) ⇒ \(\frac{dy}{dx}(3x^2y^2+x)=-(y+2xy^3)\) ⇒ \(\frac{dy}{dx} = \frac{-y+2xy^3}{x+3x^2y^2}\)

Answer»

x²y³ + xy = 1

Differentiating both sides w.r.t. x

3 x²y²\(\frac{dy}{dx}+2xy^3+x\frac{dy}{dx}+y=0\)

⇒ \(\frac{dy}{dx}(3x^2y^2+x)=-(y+2xy^3)\)

⇒ \(\frac{dy}{dx} = \frac{-y+2xy^3}{x+3x^2y^2}\)

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Find \( \frac{d y}{d x}\left(x^{2} y^{2}+x y\right)=1 \)

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