What I don’t get is how you compute the derivative of x^n. It seems to me that you make the assumption that the derivative is n*x^(n-1), put that in and arrive at your assumption. I guess I’m missing something here.
I tried to compute the derivative of f(x)=a^x (for some constant a),
starting with
f’(x) dx = f(x + dx) – f(x) = a^(x + dx) – a^x
Now, I know that I can express a^(x + dx) by a^x + f’(x) dx, but that only leads me back to f’(x) = f’(x). What would be the next step to complete the derivation?

Thank you for your prompt reply and encouragement!

Though the Amazon.com reviews of Calculus Demystified weren’t very positive, by and large, the Schaum’s outline series looks good. The Life of Fred series, which was recommended to me in the past, also looks like it might be a winner.

It’s good to hear both that it’s likely possible to avoid a study of classical mathematics in order to be able to get to intuitionist mathematics, and also that my concern about potential difficulties unlearning the classical stuff wasn’t unfounded.

Again, thanks!

Since you are coming from the philosophical angle I definitely suggest that you have a look at Erret Bishop’s manifesto, which is the introduction to his Foundations of Constructive Analysis.

It is a complete lie that you have to study classical mathematics in order to be able to later get to intuitionistic mathematics. Quite the contrary, once your brain has been trained how to use the law of excluded middle it is a real effort to deprogram yourself and be able to reason constructively. Your teachers were just trying to shut you up.