A particle moves in the plane so that its coordinates satisfy and

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A particle moves in the plane so that its coordinates satisfy x(5)=4x(5)=4 and y(5)=10y(5)=10. At time t=5t=5, the rates are dxdt=3 units s−1\dfrac{dx}{dt}=3\text{ units s}^{-1} and dydt=−2 units s−1\dfrac{dy}{dt}=-2\text{ units s}^{-1}. Let s(t)=y(t)x(t)s(t)=\dfrac{y(t)}{x(t)}. What is dsdt\dfrac{ds}{dt} at t=5t=5? (a) −192-\dfrac{19}{2} (b) 198\dfrac{19}{8} (c) −198-\dfrac{19}{8} (d) −23-\dfrac{2}{3}

Related theory

Browse the problem library