I know an Operator A is linear if A(f+g)=Af+Ag and A(cf)=cAf

Let L=linear space={f(x):x in [0,1],f'(x) exists}

Define as as follow: Af(x)=f(x)-f'(x). Is this linear operator? explain your answwer.

I thought operator can only be on the form d/dy

thanks for any help.