A sensor tracking the movement of a robotic probe in a research lab models the horizontal displacement xxx and vertical displacement yyy at time ttt using the parametric equations
x=7×6−t+3 x = 7 \times 6^{-t} + 3 x=7×6−t+3 y=4×6t−5 y = 4 \times 6^{t} - 5 y=4×6t−5Show that dydx=−47×62t\dfrac{dy}{dx} = -\dfrac{4}{7} \times 6^{2t}dxdy=−74×62t.
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.