Answer
a) $\frac{dy}{dt} = \frac{24}{25} $ in/sec
b) $\frac{dy}{dt} = 0 $ in/sec
c) $\frac{dy}{dt} = -\frac{24}{25} $ in/sec
Work Step by Step
y = $\frac{1}{1+x^2}$
$\frac{dy}{dt} = -(1+x^2)^-2*(2x) \frac{dx}{dt} = \frac{-2x}{(1+x^2)^2} \frac{dx}{dt}$
when dx/dt = 6 in/sec
a) x = -2
$\frac{dy}{dt} = \frac{-2(-2)}{(1+(-2)^2)^2}(6) = \frac{24}{25}$
b)x = 0
$\frac{dy}{dt} = \frac{-2(0)}{(1+(0)^2)^2}(6) = 0$
c) x = 2
$\frac{dy}{dt} = \frac{-2(2)}{(1+(2)^2)^2}(6) =- \frac{24}{25}$
