I am trying to differentiate the functions xn, eax and ln(ax) from first principles. I have successful in all three, but here's my problem. In finding the limit in each problem, you need to first Taylor expand to remove Δx from the denominator. But the very process of Taylor expansion uses differentiation to find its coefficients. So, it doesn't help if I am trying, for instance, trying to differentiate eax from first principles using Taylor expansion as I have used the derivative of eax itself in its differentiation. Any help on this would be great!