Mathematics

Problem

A particle moves along the ellipse

9x^{2}+4y^{2}=36

. When the particle is in the first quadrant with

x=1\,\text{unit}

and

\dfrac{dx}{dt}=2\,\text{units s}^{-1}

, what is

\dfrac{dy}{dt}

? a)

\sqrt{3}\,\text{units s}^{-1}

-\dfrac{2\sqrt{3}}{3}\,\text{units s}^{-1}

-\sqrt{3}\,\text{units s}^{-1}

-3\sqrt{3}\,\text{units s}^{-1}