Differntiation Problem

1. Nov 1, 2009

jameswill1am

1. The problem statement, all variables and given/known data

Compute $$\frac{d}{dx}\left(\frac{x^{n}\left(x-1\right)^{n}}{n!} \times e^{x}\right)$$

2. Relevant equations

$$\left(\frac{x^{n}\left(x-1\right)^{n}}{n!} \times e^{x}\right)$$

3. The attempt at a solution

I got a solution of sorts applying the product rule and then applying the product rule again but it seemed awfully messy and i was wondering what the correct solution is and if there are steps taken to tidy all this up and give a nicer answer

Thanks

2. Nov 1, 2009

Mechdude

Would you mind posting your answer? It may be ok, $$\frac {x^{n-1}(x-1)^{n}e^{x}}{(n-1)!} + \frac {x^{n}(x-1)^{n-1}e^{x}}{(n-1)!} + \frac {x^{n}(x-1)^{n}e^{x}}{(n)!}$$