- #1

Calcgeek123

- 20

- 0

## Homework Statement

Given: the integral from 0 to infinity of t^(x)e^(-t)dt

Problem: Determine f'(x).

## Homework Equations

## 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 that's 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.