Prove that if $f$ is an odd function, then $f ′ (x) = f ′ (- x)$.
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4Does this answer your question? Derivative of an even function is odd and vice versa – Physical Mathematics Apr 22 '20 at 02:11
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If f is odd -f(x)=f(-x) – uhhhhidk Apr 22 '20 at 02:11
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@uhhhhidk no, that is if $f$ is even. – Bernkastel Apr 22 '20 at 02:12
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1@Dunkelheit -f(x)=f(-x) is the definition of an odd function – uhhhhidk Apr 22 '20 at 02:16
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@uhhhhidk That pencil on the right of your comment means that it was edited, it's not a shame to say that one can make mistakes (even just typo). – Bernkastel Apr 22 '20 at 02:25
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@Dunkelheit I admit I typed that in at first but you commented after I changed it so I assumed you misread it or something, it might’ve taken longer than I expected – uhhhhidk Apr 22 '20 at 06:09
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If $f$ is odd then $f(-x)=-f(x)$ for all $x$ in the domain of $f$; now you can take the derivative (because $f$ must be at least derivable or this question has no sense) of both sides and get (for the chain rule) $$-f'(-x)=-f'(x)\Rightarrow f'(-x)=f'(x)$$
amWhy
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Bernkastel
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