1. The problem statement, all variables and given/known data The cissoid of Diocles is given by the relation y2(2-x) = x3. Find the equation to the tangent line to the curve at the point (1,1). 2. Relevant equations 3. The attempt at a solution Solution d/dx [ y2(2-x) ] = d/dx [ x3 ] 2y dy/dx (2-x) + y2(-1) = 3x2 Therefore, dy/dx = 3x2+y2 / 2y(2-x) m = dy/dx | (1,1) = 3+1/2(1) = 2 so y=2x+c and y(1) = 1, therefore 1=2+c ==> c=-1 Equation is y=2x-1 My attempt y2(2-x) = x3 2y2-xy2-x2=0 d/dx [2y2-xy2-x3 = d/dx  4y*dy/dx-y2-2xy*dy/dx-3x2 = 0 dy/dx [ 2xy - 4y ]-y2-3x2 dy/dx = -y2-3x2 / 2xy-4y My solution gives m=1, therefore y=mx+c, 1=1*1+c, c=0 y=1... The problem I'm having is that I don't understand why I can't expand the brackets in the original relation, y2(2-x) to be 2y2-xy2 or subtract x3 from both sides to make the equation 2y2-xy2-x2=0, which in my mind would make the problem easier to solve.