The equation of a curve is x(y^2)=x^2 +1 . Using the differential, find the coordinates of the stationary point of the curve.

Firstly we need to use product rule to find the dy/dx of the left hand side (LHS). Using implicit differentiation, we know the differential of y^2 is 2y(dy/dx). Then use to product rule to obtain the dy/dy of LHS to be 2xy(dy/dx). The right hand side, we can treat as a normal differential therefore it is 2x. We can then rearrange the equation so that (dy/dx) is the subject. Now, we need to find the stationary point and to do that, we must set the differential equal to zero and rearrange to get either x or y on its own. I suggest trying to isolate y since it makes the next part a little easier. After rearranging, you should get y=root2x so then we can substitute root2x into the original equation to get the x coordinate. This is 1. To obtain the y coordinate, simply sub 1 into our equation for y and we get +/- root2.