Thanks for the feedback. I reformatted my problem to be a single ODE, solved with DESolve, and tried to plot the results via MAPLE's help file, and it still didn't work. My code is below. As you can see from the chart, the function m(t) is clearly changing, so I would expect to see the derivative plot, but I can't seem to get it out.
mtest := [diff(m(t), t) = -43/25*exp(-8527.784461/(378.15+240*t)+19.03523317)*(m(t)-exp(-23300/(3143.93910+1995.360*t)+2.646139043)), m(0) = 1]
sol1 := dsolve(mtest,type=numeric, range=0..1);
plots[odeplot](sol1, [[t, m(t), color = blue], [t, diff(m(t), t), color = blue]], 0 .. 1);
I'm baffled. This should be easy, but it's like I'm not catching something simple...