Answer
$\frac{dy}{dt} = \frac{-3}{2}$
Work Step by Step
Given that $\frac{dx}{dt} = -2$ and $x^2+y^2=25$
on differentiating with respect to time
$\frac{dx^2}{dt} + \frac{d y^2}{dt} = \frac{d25}{dt}$
$2x\frac{dx}{dt} + 2y\frac{dy}{dt} =0 $
when x=3, y=-4
then $ -8\frac{dy}{dt} - 2\times (-2)\times3=0$
$\frac{dy}{dt} = \frac {-3}{2}$
Thus, the answer is $\frac{dy}{dt} = \frac{-3}{2}$
