Find dy/dx when x+2y+3y^2= 2x^2+1

To solve this question we can use implicit differentiation. We can write:d/dx(x+2y+3y^2)=d/dx(2x^2+1).When differentiating something in terms of y with respect to x we can use the chain rule, this allows us to differentiate with respect to y and multiply by dy/dx. 1+(d(2y)/dy)*dy/dx+(d(3y^2)/dy)*dy/dx=4x, then we differentiate our y values with respect to y: 1+2dy/dx+(6y)dy/dx=4x. Then we need to set dy/dx as the subject of the equation:dy/dx(2+6y)=4x-1, then by dividing each side by (2+6y) we get dy/dx=(4x-1)/(2+6y).