showing f'(-x)=f'(x)

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October 25th 2007, 10:57 PM
unluckykc

showing f'(-x)=f'(x)

Show that the derivative of an odd function is even. That is, if f(-x)=-f(x), then f'(-x)=f'(x). Without using a specific example.
October 26th 2007, 03:45 AM
Plato

$f\left( { - x} \right) = - f(x)$
$D_x \left( {f\left( { - x} \right)} \right) = f'( - x)( - 1) = - f'( - x)$
$D_x \left( { - f\left( x \right)} \right) = - f'(x)$
$f'(x) = f'( - x)$
October 26th 2007, 07:15 AM
unluckykc

I don't understand how you got the last line. How does f'(x)=f'(-x)?
October 26th 2007, 08:14 AM
Plato

$\begin{array}{l}<br /> - f'( - x) = D_x (f( - x)) = D_x ( - f(x)) = - f'(x) \\ <br /> f'( - x) = f'(x) \\ <br /> \end{array}<br />$

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