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

1. 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.

2. $f\left( { - x} \right) = - f(x)$
$D_x \left( {f\left( { - x} \right)} \right) = f'( - x)( - 1) = - f'( - x)$
$D_x \left( { - f\left( x \right)} \right) = - f'(x)$
$f'(x) = f'( - x)$

3. I don't understand how you got the last line. How does f'(x)=f'(-x)?

4. $\begin{array}{l}
- f'( - x) = D_x (f( - x)) = D_x ( - f(x)) = - f'(x) \\
f'( - x) = f'(x) \\
\end{array}
$