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