Answer
$\frac{dy}{dt}=-64$
Work Step by Step
$y^{2} - 8x^{3}= -55$
$2y\frac{dy}{dt}-24x^{2}\frac{dx}{dt}=0$
Now substitute x = 2, y = 3, and dx/dt = -4 to get
$2(3)\frac{dy}{dt}-24(2)^{2}(-4)=0$
$\frac{dy}{dt}=-64$
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