A curve has equation
y2=ye3x+2x y^2 = y e^{3x} + 2x y2=ye3x+2xShow that
dydx=3ye3x+22y−e3x \frac{dy}{dx} = \frac{3y e^{3x} + 2}{2y - e^{3x}} dxdy=2y−e3x3ye3x+2The curve crosses the yyy-axis at the origin (0,0)(0, 0)(0,0) and at a second point PPP. The tangent to the curve at the origin and the tangent to the curve at PPP meet at the point RRR. Find the coordinates of RRR.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions 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), matched to the AQA A Level Maths (7357) 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.
