Plotted function returning unexpected result

I am currently doing a little project which involves using a defined function. I set values for two terms, and I took the derivative and squared the two terms. When I attempt to plot it, I do not get anything in the window, nor do I get any errors. Here is what I have for code:

a = ((1/8)*(((0.1*t) - 3)^5)) - 0.5*(((0.1*t) - 3)^3)
b = ((0.1*t) - 3)^2
e = Sqrt[((a')^2) + ((b')^2)]

I receive the following output for the solution of "e"

Sqrt[(Derivative[(-0.5 (-3 + 0.1 t)^3 + 1/8 (-3 + 0.1 t)^5)])^2 + (Derivative[((-3 + 0.1 t)^2)])^2]

When I go to plot:

Plot[e, {t, 0, 60}, AspectRatio -> 0.5, Frame -> True]

I get a graph with no plot.

Is there something I am doing wrong? Any help would be appreciated.

• Have a look at a specific value, e[1.23] for instance, for a hint. – b.gates.you.know.what Apr 19 '18 at 12:18
• When I do that, I just get whatever I got for "e" with a [1.23] stuck at the end of it. – Apple Cola Apr 19 '18 at 12:26
• What are the primes (') are suppose to do? You probably want e = Sqrt[(D[a,t]^2) + (D[b,t]^2)]... – Henrik Schumacher Apr 19 '18 at 12:45
• Yeah, you were right. I used that prime notation for another project, but I guess it was just a matter of syntax. Thanks! – Apple Cola Apr 19 '18 at 13:05 