A magnetic field is modeled such that a specific field line CCC follows the equation
4x+5y2+2xy2=10(5x)+10,y>0 4x + 5y^{2} + 2xy^{2} = 10(5^{x}) + 10, \quad y > 0 4x+5y2+2xy2=10(5x)+10,y>0where xxx and yyy are distances in centimeters.
Determine an expression for dydx\frac{dy}{dx}dxdy in terms of xxx and yyy.
The field line CCC crosses the yyy-axis at the point PPP.
Find the exact value of the gradient of the field line at PPP.
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.
