The point P P\,P lies on the curve with equation y=xex2y = xe^{x^2}y=xex2 with x x\,x coordinate 1
Find an equation to the tangent to the curve at the point PPP.
The tangent intersects the x x\,x axis at the point A A\,A and the y y\,y axis at the point BBB. Find the exact area of the triangle AOBAOBAOB, where O O\,O is the origin.