Mass distribution of a semi-infinite stick

[Jzhang27143]

Homework Statement

Given a semi-infinite stick (that is, one that goes off to infinity in one direction), determine how its density should depend on position so that it has the following property: If the stick is cut at an arbitrary location, the remaining semi-infinite piece will balance on a support that is located a distance l from the end.

http://www.personal.kent.edu/~fwilliam/Chapter 1 Statics.pdf - Problem 18

Homework Equations

T = r x F

The Attempt at a Solution

In the linked solution, I understand the setup, but I do not understand how to find the derivative of the integral with respect to x0. Can someone give me a more detailed explanation of this step?

 

[haruspex]

Do you understand how to differentiate an integral with respect to a variable that occurs (1) within the integrand only (2) in one or both bounds (3) in all three places?
If not, take a look at http://en.m.wikipedia.org/wiki/Differentiation_under_the_integral_sign