How would you prove that if is an even function ( ) and has a derivative at every point, then the derivative is an odd function ( ) ?

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- Mar 22nd 2010, 04:40 AMfrenchguy87Even/odd function differentiability
How would you prove that if is an even function ( ) and has a derivative at every point, then the derivative is an odd function ( ) ?

- Mar 22nd 2010, 05:16 AMtonio
- Mar 22nd 2010, 06:44 PMfrenchguy87
- Mar 22nd 2010, 08:48 PMtonio
- Mar 24th 2010, 07:03 PMfrenchguy87
I don't know why but I'm not convinced

- Mar 24th 2010, 08:30 PMtonio
- Mar 24th 2010, 09:21 PMTinyboss
Tonio gave the true answer. If you need some intuition, just draw an even function (symmetric around the y-axis) and pick some point x. Then draw tangent lines at x and at -x. Clearly they have opposite slopes.