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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 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.
