How can I define an abstract odd function in mathematica? With respect to derivatives -


i want "to work symbolically" not function derivatives. instance 

f'[x] - f'[-x]

to simplified zero.

comment: neither of ways, suggested here, did not me.

they kind of works need create rules derivative not f really. , since derivative not protected can like:

derivative[n_][f][-x_] := -derivative[n][f][x]  f''[x] + f'''''''[-x] + f''[-x] + f[x] + f'''''''[x] 
f[x]

is ok?


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