Mathematics

Problem

Suppose

x

and

y

are differentiable functions of time

t

linked by

x^{2}y=10

. If

\dfrac{dx}{dt}

is known, which expression gives

\dfrac{dy}{dt}

in terms of

x

y

, and

\dfrac{dx}{dt}

? a)

\displaystyle \frac{dy}{dt}=\frac{2y}{x}\,\frac{dx}{dt}

\displaystyle \frac{dy}{dt}= -\frac{2y}{x}\,\frac{dx}{dt}

\displaystyle \frac{dy}{dt}= -\frac{2x}{y}\,\frac{dx}{dt}

\displaystyle \frac{dy}{dt}= -\frac{y}{x}\,\frac{dx}{dt}