Hi all. For any of you who have done differential calculus, I need a little help with a problem involving natural logarithms. The question asks to differentiate y = ln x from first principles . It says "use the definition of the Euler number, namely e = lim(n->inf.) (1+1/n)^n.". First principles means f'(x) = lim(h->0) [f(x+h) - f(x)] / h (this is the first thing we learned in calculus). I so far managed two different methods: Method 1. y = ln x therefore e^y = x dx/dy = e^y. Since dx/dy * dy/dx = 1 1/(dx/dy) = dy/dx. = 1/e^y = 1/x. Method 2. y = ln x f(x) = ln x f(x+h) = ln (x+h) f'(x) = lim(h->0) [ln (x+h) - ln x] / h = lim(h->0) ln (x+h/x) / h = lim(h->0) 1/h * ln(1+h/x) Since lim(h->0) ln(1+h/x) -> h/x where h != 0, f'(x) = 1/h * h/x = 1/x Both of these methods work and are valid, although I didn't bring the definition of the Euler number into it. I personally have no idea how to do this. Could anyone here who has done a bit of math before please help me with this? Thanks.