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**x d/dx**(where 1st

*d/dx*acts on the function, then

*x*acts on the resulting function by simply multiplying by

*x*)acting on the set of functions of a real variable

*x*for

*x>0*. What are the eigenvalues and the corresponding eigenfunctions of this operator?

b) What about

**d/dx x**(where 1st

*x*acts on the function, then

*d/dx*acts upon the resulting function)? What are the eigenvaules and corresponding eigenfunctions for this?