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Math Help - function odd derivative

  1. #1
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    function odd derivative

    function f: R.....R called even if f(x)=f(-x) all x belongs R .function g : R.....R called odd if g(x)= -g( -x) all x belongs R .show with help of difinition of derivative that the derivative of an even deriverbar function is an odd function .


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  2. #2
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    Quote Originally Posted by hoger View Post
    function f: R.....R called even if f(x)=f(-x) all x belongs R .function g : R.....R called odd if g(x)= -g( -x) all x belongs R .show with help of difinition of derivative that the derivative of an even deriverbar function is an odd function .


    thank you
    For an even function f(x) :

    f'(-x)=\lim_{h\to 0} \frac{f(-x+h)-f(-x)}{h}= \lim_{h\to 0} \frac{f(x-h)-f(x)}{h}=-\lim_{h\to 0} \frac{f(x)-f(x-h)}{h}=-f'(x)

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