L'Hopital Help Please! Find the limit as x approaches infinity of x^((ln 2)/(1 + ln x))?

Question

I've tried infinity, -infinity, 0, and 1, but stupid Webassign says it's wrong, I've taken it to the 3rd derivation with L'Hopital's but nothing works.

Answer 1

Differentiate the numberator and the denominator.
the derivative of x^k = x^k (ln (k)
ln[ln(2)]x^(ln(2) /(1+1/x)
as x-> infinity the denominator approaches 1, but the numerator approaches infinity.
My guess is 'infinity.'
If you keep differentiating, the same thing would occur again.

Answer 2

= lim x--> infinity [ln(2)x^(ln (2) -1)]/1/(x(1+lnx))= infinity