To get the derivative of you can use logarithmic differentiation.
Edit: My mistake: , NOT e. l'H CANNOT be used. See post #4.
To get the derivative of :
So the limit becomes:
Now show that .
Multiple applications of l'Hospital's rule is one possible approach.
Another approach is to substitute the series expansion for ln (1 + x): . This substitution is valid since the series converges for and ......