Mathematics

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}

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

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

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