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f(x)=e^(-1/x),w h e r ex >0, Let for eac...

`f(x)=e^(-1/x),w h e r ex >0,` Let for each positive integer `n ,P_n` be the polynomial such that `(d^nf(x))/(dx^n)=P_n(1/x)e^(-1/x)` for all `x > 0.` Show that `P_(n+1)(x)=x^2[P_n(x)-d/(dx)P_n(x)]`

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The correct Answer is:
`x^(2)[P_(n)(x)-(dP_(n)(x))/(dx)].`
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