1. The problem statement, all variables and given/known data Given: the integral from 0 to infinity of t^(x)e^(-t)dt Problem: Determine f'(x). 2. Relevant equations 3. The attempt at a solution My teacher mentioned using the definition of a derivative: f'(a)= limit as x approaches a of f(x)-f(a)/(x-a). So far I have: f'(a)=the integral of the limit as x approaches a of t^(x)e^(-t)-t^(a)e^(-t)/(x-a) dt. I'm not sure where to go from here, or if thats even correct. I think it should end up being f'(x)=t^(x)e^(-t) which makes sense to me. I'm just not sure how to actually get there. Thank you to all.