The cross-section of a custom aerodynamic fairing is modeled by a curve with equation
2y2+3x=4ye0.5x 2y^2 + 3x = 4ye^{0.5x} 2y2+3x=4ye0.5xDetermine an expression for dydx\frac{dy}{dx}dxdy in terms of xxx and yyy.
The curve intersects the yyy-axis at the origin and at a point PPP.
Find the equation of the normal to the curve at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c where mmm and ccc are constants to be found.
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.
