int xe^xe^x-1^12

We can start by using the quotient rule for differentiation:

f(x) = (x*e^(x))/(e^(x)-1)^(1/2)

f'(x) = [(e^(x)-1)^(1/2)(e^(x)+xe^(x)) - (xe^(x))(1/2)(e^(x)-1)^(-1/2)(e^(x))] / (e^(x)-1)

Simplifying this expression, we get:

f'(x) = [e^(x)(e^(x)-1)^(1/2) + xe^(2x)*(e^(x)-1)^(1/2)] / (e^(x)-1)^(3/2)

This is the final answer.