Okay, it's late, but I started with the question of f'(ln x): f'(ln x) = lim(h -> 0) ( [f(x0 + h) - f(x0)] /h ) = lim(h -> 0) ( [ln(x0 + h) - ln(x0)] /h ) = lim(h -> 0) ( ln( [x0 + h] / x0) /h ) Will have a closer look later. Gotta revise some log rules. Indeed ln x is logarithmus naturalis == log of x, base being e.