Can somebody check my solution please?

$\displaystyle

1 - x/1! + x(x-1)/2! +..+(-1)^n x(x-1)(x-2)....(x-n+1)/n!

$

$\displaystyle

= (-1)^n x(x-1)(x-2)....(x-n)/n!

$

Proof: by using derivation I will show that 1,2,3,,,n are simple roots of both polynomials, that implies they must be equal

Am I right? Thank you very much.