What is the implicit derivative of 5=xy^3-x^2y+3xy5=xy3x2y+3xy?

1 Answer
Apr 20, 2018

dy/dx=(2xy-3y-y^3)/(3xy^2-x^2+3x)dydx=2xy3yy33xy2x2+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+3y0=3xy2dydx+y3x2dydx2xy+3xdydx+3y

rArrdy/dx(3xy^2-x^2+3x)=2xy-3y-y^3dydx(3xy2x2+3x)=2xy3yy3

rArrdy/dx=(2xy-3y-y^3)/(3xy^2-x^2+3x)dydx=2xy3yy33xy2x2+3x