I finally figured out in the assignment I'm doing that one of the variables, known as e, is the e. I.e., it's not actually a variable.
I gather (but can't prove) that of the properties of e is that"
Having forgotten that e is not just a regular variable, I decided to take the derivative the old-fashioned way:
This leads me astray. Plugging in x=2, I find that ordinary derivation gives me:
and I'm pretty sure
only when e=2. And because this is the e, it doesn't equal 2!
I can solve the problem now, only I have somewhat less faith in my new ability (?) to take a basic derivative. Is it just that ordinary derivation doesn't work with transcendental / irrational numbers, or did I derive wrong?
Recall the chain rule.