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## Homework Statement

Show [tex]\left[x,f(p)[/tex][tex]\right)][/tex] = [tex]i\hbar\frac{d}{dp}(f(p))\right.[/tex]

## Homework Equations

I can use [tex]\left[x,p^{n}[/tex][tex]\right)][/tex] = [tex]i\hbar\\n\right.[/tex][tex]p^{n}\right.[/tex]

f(p) = [tex]\Sigma[/tex] [tex]f_{n}[/tex][tex]p^{n}[/tex] (power series expansion)

## The Attempt at a Solution

I started by expanding f(p) to the power series which makes

[tex]\left[x,\Sigma\\f_{n}\\p^{n}[/tex][tex]\right)][/tex]

and I know I must use the commutator identity [A, BC] = [A,B]C + B[A,C]

but the power series cannot be split up into two products(BC) ? So I'm not sure how to go on