Prove the function:

-sum_i(x_i*ln(x_i))

is convex for x>0

I have graphed the function, and can see visually that it is convex, but I don't know how to prove that it is convex. If I graph the slope of the graph between any two points, it seems like the slope is always decreasing. This seems like a way to prove it visually, but how can I put that into a mathematical proof?