Quick (& Easy) Derivative Clarification

Hello and thanks in advance for your help.

I'm studying how derivatives are reflected in the shape of a function's graph and am doing pretty well with it, but had one clarifying question.

Am I right in saying that if my given function f(x) = e^2x + e^-x, then...

f'(x) = e^2x - e^-x

f''(x) = e^2x + e^-x ?

I'm mostly looking to confirm that those are right, but I'd like to understand better why the derivative of e^-x = -e^-x while the derivative of e^x = e^x.

Thanks for any explanations/corrections!