The point P P\,P lies on the curve with equation y=xe2x2y = xe^{2x^2}y=xe2x2 with xxx-coordinate 1.
Find an equation of the tangent to the curve at the point PPP.
The tangent intersects the xxx-axis at the point A A\,A and the yyy-axis at the point BBB. Find the exact area of the triangle AOBAOBAOB, where O O\,O is the origin.