Show that the polynomial
\[L_n(x) = \sum_{k=0}^{n} (-1)^k {n \choose k} \frac{x^k}{k!}\]
is an eigenfunction of the symmetric operator
\[D(f(x)) = xf^{\prime \prime}(x)+(1-x)f^{\prime}(x)\]
I know that to show this, I need to solve the following equation for lambda:
\[D(L_n) = \lambda L_n\]
So I just plug the polynomial into the equation and... dang, I don't know how differentiate the polynomial :( Can someone suggest a derivative of the polynomial or some workaround?

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