The lateral displacement, xxx mm, of a high-precision vibrating needle is modeled by the equation
x=14cos2(4y)0<y<π8 x = 14 \cos^2(4y) \qquad 0 < y < \frac{\pi}{8} x=14cos2(4y)0<y<8πwhere yyy is the angle of the driving cam in radians.
Show that the rate of change of the cam angle with respect to displacement is given by
dydx=−1ABx−x2 \frac{dy}{dx} = -\frac{1}{A\sqrt{Bx - x^2}} dxdy=−ABx−x21where AAA and BBB are integers 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.
