A streamline of fluid flow in a microfluidic device follows a path described by the curve with equation
3y2+8x=3ye−4x 3y^2 + 8x = 3ye^{-4x} 3y2+8x=3ye−4xFind dydx\frac{dy}{dx}dxdy in terms of xxx and yyy.
The path crosses the vertical axis at the origin and at a point PPP.
Find the equation of the normal to the streamline at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c where mmm and ccc are constants to be determined.
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.
