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.
717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.