How to Find dy/dx, Implicit differentiation? 2xy^3 + y = 2x

1 Answer
Jun 25, 2018

dy/dx= (2-2y^3)/(6xy^2+1)dydx=22y36xy2+1

Explanation:

  1. d/dx(2xy^3+y)=d/dx*2xddx(2xy3+y)=ddx2x

  2. 2*d/dx(xy^3)+d/dx*y=22ddx(xy3)+ddxy=2

  3. Use product rule on first differential

2*(3xy^2*dy/dx+y^3)+dy/dx=22(3xy2dydx+y3)+dydx=2

  1. Expand

6xy^2*dy/dx+2y^3+dy/dx=26xy2dydx+2y3+dydx=2

  1. Collect like terms

(6xy^2+1)*dy/dx+2y^3=2(6xy2+1)dydx+2y3=2

Solve for dy/dxdydx

dy/dx=(2-2y^3)/(6xy^2+1)dydx=22y36xy2+1