The coordinates of a moving point satisfy

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The coordinates

(x,y)

of a moving point satisfy

x^{2}y+y^{3}=10

. At the instant when

x=1

y=2

and

\dfrac{dx}{dt}=5\,\text{units s}^{-1}

, determine

\dfrac{dy}{dt}

. (a)

-\dfrac{5}{3}\,\text{units s}^{-1}

(b)

\dfrac{20}{13}\,\text{units s}^{-1}

(c)

-\dfrac{20}{13}\,\text{units s}^{-1}

(d)

-\dfrac{20}{7}\,\text{units s}^{-1}