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Question Number 95635 by Ar Brandon last updated on 26/May/20
Show that if a function is even and derivable then f′(x) is an odd function.
Showthatifafunctionisevenandderivablethenf′(x)isanoddfunction.
Answered by mr W last updated on 26/May/20
f(x) is even: f(−x)=f(x) f′(−x)=((df(−x))/(d(−x)))=−((df(x))/dx)=−f′(x) ⇒f′(x) is odd.
f(x)iseven:f(−x)=f(x)f′(−x)=df(−x)d(−x)=−df(x)dx=−f′(x)⇒f′(x)isodd.

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