For the ellipse

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

Problem

For the ellipse

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

, a point is in the first quadrant with

y=2

and

\dfrac{dy}{dt}=2\text{ units/s}

. What is the corresponding value of

\dfrac{dx}{dt}

? (a)

-\dfrac{4\sqrt5}{15}\text{ units/s}

(b)

\dfrac{8\sqrt5}{15}\text{ units/s}

(c)

-\dfrac{8\sqrt5}{15}\text{ units/s}

(d)

-\dfrac{8\sqrt5}{45}\text{ units/s}