Find dy/dx of the equation (x^3)*(y)+7x = y^3 + (2x)^2 +1 at point (1,1)

Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side of the equation and factor them out. Divide the factor through, to give the answer. (Demonstrate on white board) Put in x = 1 and y = 1 in to the equation to yield the answer. dy/dy = 1.