4x^3 + ln(y^2) + 2y = 2x Use implicit differentiation to find dy/dx

Find (dy)/(dx) if 4x^3+lny^2+2y=2x
Rewrite the second term using a property of logarithms:
4x^3+2lny+2y=2x
Divide through by 2:
2x^3+lny+y=x
Differentiate term by term with respect to x:
6x^2+1/y*(dy)/(dx)+(dy)/(dx)=1
(dy)/(dx)(1/y+1)=1-6x^2
(dy)/(dx)=(1-6x^2)/(1/y+y)
(dy)/(dx)=(y-6x^2y)/(1+y^2)

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