How do I find dy/dx for the following equation: (x^2) + 2y = 4(y^3) + lnx?

This is an example of implicit differentiation with respect to x.The technique for differentiating such an equation is as follows:1. Differentiate each term in x with respect to x.2. For each term in y, differentiate with respect to y, and multiply the result by dy/dx.3. Rearrange the resulting equation, to make dy/dx the subject of the formula.Solution:Let equation (x^2) + 2y = 4(y^3) + lnx be called ().Differentiating () with respect to x, then rearranging, according to the three rules above, gives:2x + 2(dy/dx) = 12(y^2) + (1/x) =>2 - 12(y^2) = (1/x) - 2x =>21 - 6(y^2) = [1 - 2(x^2)]/x =>dy/dx = [1 - 2(x^2)]/(2x[1 - 6(y^2)]).