Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x3y2 − x4y + 4xy3 = 0

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02-10-2017
Mathematics

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Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x3y2 − x4y + 4xy3 = 0

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jdoe0001 jdoe0001 · Answer 1 · 2017-10-02T02:00:34+02:00

[tex]\bf x^3y^2-x^4y=4xy^3=0\\\\ -------------------------------\\\\ \left( 3x^2y^2+x^32y\frac{dy}{dx} \right)-\left( 4x^3y+x^4\frac{dy}{dx} \right)+4\left( 1\cdot y^3+x3y^2\frac{dy}{dx} \right)=0 \\\\\\ 2x^3y\frac{dy}{dx}-x^4\frac{dy}{dx}+12xy^2\frac{dy}{dx}=4x^3y-3x^2y^2-4y^3 \\\\\\ \cfrac{dy}{dx}\left( 2x^3y-x^4+12xy^2 \right)=4x^3y-3x^2y^2-4y^3 \\\\\\ \cfrac{dy}{dx}=\cfrac{4x^3y-3x^2y^2-4y^3}{2x^3y-x^4+12xy^2}[/tex]