How do you define an abstract odd function in mathematics? With regard to derivatives

I want to "work symbolically", but not only with a function, but also with derivatives. For example, I would like

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


to simplify to zero.

Commentary: None of the ways suggested here helped me.


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1 answer

They seem to work, but now you need to create rules for Derivative

not before f

. And since Derivative

it is not protected, you can do something like:

Derivative[n_][f][-x_] := -Derivative[n][f][x]

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




this is normal?



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