Assume that the temperature of a person during an illness is given by $T(t) = \frac{9t}{t^2 + 1} + 98.6$, where T is the temperature, in degrees Fahrenheit, at time t, in hours. Find the rate of change, $\frac{dT}{dt}$, of the temperature with respect to time, using Quotient Rule.
$\frac{dT}{dt} = \frac{9(1 - t^2)}{(t^2 + 1)^2}$
$\frac{dT}{dt} = \frac{9}{t^2 + 1}$
$\frac{dT}{dt} = \frac{9(t^2 - 1)}{(t^2 + 1)^2}$
$\frac{dT}{dt} = \frac{9(1 - t^2)}{(t^2 + 1)^2}$
