证明若函数f(x)在R上是可导的奇函数,则f'(x)在R上是偶函数.

f'(x)=【f(x+⊿x）-f(x)】/⊿x ,⊿x趋近去0时的极限f'(-x)=lim【f(-x+⊿x）-f(x)】/⊿x ,把⊿x换为-⊿x,得f'(-x)=【f(-x-⊿x）-f(x)】/-⊿x=【-f(x+⊿x）+f(x)】/-⊿x=【f(x+⊿x）-f(x)】/⊿x=f'(x),所以是偶函数...