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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 100 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.