Find (dy)/(dx) implicit differentiation if xy + y ^ 3 = 4x - 3 using implicit differentiation.

xy + y ^ 3 = 4x - 3

 

\(x\frac{dy}{dx}+1\cdot y+3y^2\frac{dy}{dx}=4\\~\\ (x+3y^2) \frac{dy}{dx}+y=4\\~\\ \frac{dy}{dx}=\frac{4-y} {x+3y^2} \\~\\\)

 

where  \(x\ne -3y^2\)