1.Evaluate: (1/(x*sqrt(x^2-4))

Question

I know the answer is -1/2*arctan(2/sqrt(x^2-4)), but I am having trouble getting to this answer on my own.

I know the formula to solve it is 1/a*arctan(x/a) and that a=2, but that's all I know.

2.Find the limit of x^((ln 2)/(1+ln(x))) as x approaches negative infinity.