What is the implicit derivative of 5=xy^3-x^2y+3xy5=xy3−x2y+3xy?

1 Answer
Jim G.
Apr 20, 2018

dy/dx=(2xy-3y-y^3)/(3xy^2-x^2+3x)dydx=2xy−3y−y33xy2−x2+3x

Explanation:

"differentiate the 3 terms on the right using "color(blue)"product rule"differentiate the 3 terms on the right using product rule

rArr0=3xy^2dy/dx+y^3-x^2dy/dx-2xy+3xdy/dx+3y⇒0=3xy2dydx+y3−x2dydx−2xy+3xdydx+3y

rArrdy/dx(3xy^2-x^2+3x)=2xy-3y-y^3⇒dydx(3xy2−x2+3x)=2xy−3y−y3

rArrdy/dx=(2xy-3y-y^3)/(3xy^2-x^2+3x)⇒dydx=2xy−3y−y33xy2−x2+3x

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