Using the definition of the derivative, prove that the derivative of an odd function is an even function.

I am confused. Does g(-x) = -f(-x) or does g(-x) = -g(-x)? You seem to be going from one to another throughout your work.
 
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You need to think what it is you want to show. You want f'(x) to be even. That is f'(x) = f'(-x).

So you start off with f'(x) and using the definition of the derivative and the fact that f(x) is an odd function and arrive at f'(-x)
 
I am confused. Does g(-x) = -f(-x) or does g(-x) = -g(-x)? You seem to be going from one to another throughout your work.
sorry about that its all g . that -f(-x) was ment to be -g(-x)
 
sorry about that its all g . that -f(-x) was ment to be -g(-x)
I realize that Jared123 is not reasonable for the wording of this question.
But that does not stop me from hating it. This is a classic question using the chain rule on the derivative of g(x)g(-x).
Here is a good page.
 
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