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.
Last edited by unluckykc; Oct 25th 2007 at 10:58 PM. Reason: I forgot to tyoe a sentence.
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$\displaystyle f\left( { - x} \right) = - f(x)$ $\displaystyle D_x \left( {f\left( { - x} \right)} \right) = f'( - x)( - 1) = - f'( - x)$ $\displaystyle D_x \left( { - f\left( x \right)} \right) = - f'(x)$ $\displaystyle f'(x) = f'( - x)$
I don't understand how you got the last line. How does f'(x)=f'(-x)?
$\displaystyle \begin{array}{l} - f'( - x) = D_x (f( - x)) = D_x ( - f(x)) = - f'(x) \\ f'( - x) = f'(x) \\ \end{array} $
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