A micro-robotic probe's position (x,y)(x, y)(x,y) in micrometres is tracked over time t t\,t seconds within a biological medium. The path is defined by the parametric equations
x=4×2−t−1 x = 4 \times 2^{-t} - 1 x=4×2−t−1 y=3×2t+5 y = 3 \times 2^{t} + 5 y=3×2t+5Show that dydx=−34×22t\dfrac{dy}{dx} = -\dfrac{3}{4} \times 2^{2t}dxdy=−43×22t.
Find the Cartesian equation of the curve in the form xy+ax+by=cxy + ax + by = cxy+ax+by=c, where aaa, bbb and ccc are integers.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.