implicit derivative of xy22y3x slope of the line tangent at

Solution

xy^2+2y=3x d(xy^2)/dx + d(2y)/dx = d(3x)/dx xd(y^2)/dx + y^2d(x)/dx + 2dy/dx=3dx/dx 2xdy/dx + y^2 + 2dy/dx = 3 (dy/dx) ( 2x+2 ) = 3-y^2 now at (1,1 ) x=1 and y=1 dy/dx = (3-y^2)/(2x+2) =(3-1)/(2+2) =2/4 =0.5