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

• 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}
- f'( - x) = D_x (f( - x)) = D_x ( - f(x)) = - f'(x) \\
f'( - x) = f'(x) \\
\end{array}
$