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

1 Answer
RedRobin9688
Jun 25, 2018

#dy/dx= (2-2y^3)/(6xy^2+1)#

Explanation:

  1. #d/dx(2xy^3+y)=d/dx*2x#

  2. #2*d/dx(xy^3)+d/dx*y=2#

  3. Use product rule on first differential

#2*(3xy^2*dy/dx+y^3)+dy/dx=2#

  1. Expand

#6xy^2*dy/dx+2y^3+dy/dx=2#

  1. Collect like terms

#(6xy^2+1)*dy/dx+2y^3=2#

Solve for #dy/dx#

#dy/dx=(2-2y^3)/(6xy^2+1)#

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