The point P P\,P lies on the curve with equation y=3xex2y = 3xe^{x^2}y=3xex2 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.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.