Differentiation Problem: Solving for d/dx in x^n(x-1)^n/n! * e^x

[jameswill1am]

Homework Statement

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

Homework Equations

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

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

 

[Mechdude]

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