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Question Number 174587 by bekzodjumayev last updated on 05/Aug/22

Commented by kaivan.ahmadi last updated on 05/Aug/22

$$f(-x)=-f\left(x\right)$$$$\Rightarrow fisanoddfunction$$$$\Rightarrow f^{\prime }\left(x\right)=f^{\prime }(-x)\Rightarrow f^{\prime }isanevenfunction$$$$\Rightarrow fof(-x)=f(-f\left(x\right))=-fof\left(x\right)$$$$\Rightarrow fofisanoddfunction$$$$\Rightarrow {\left[fof\right]}^{\prime }isanevenfunction$$$$\Rightarrow {\left(fof\right)}^{\prime }(-3)={\left(fof\right)}^{\prime }\left(3\right)$$$$\Rightarrow {\left(fof\right)}^{\prime }\left(3\right)-{\left(fof\right)}^{\prime }(-3)=0$$$$$$

Commented by bekzodjumayev last updated on 05/Aug/22

$$Thankyou$$

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