Commutators for functions of operators (momentum/position)

[Ratpigeon]

Homework Statement

show that [x,f(p_x)] = i $\hbar$ d/d(p_x) f(p_x)

Homework Equations

x is the position operator in the x direction, p_x is the momentum operator; i $\hbar$
d/dx
[x, p_x]=xp-px

The Attempt at a Solution

I'm stuck. maybe chain rule for d/dx and d/d(p_x)...? But I don't see how I'd do it...

 

[Ratpigeon]

Never mind - I had to reqresent it as a power series, and then it was easier