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Prove that the derivative of an even ...

Prove that the derivative of an even function is an odd function and that of an odd function is an even function.

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1)`f` is even : `f(-x)=f(x)`.
Example: `f(x)=x^{2}`.
Differentiate both sides:
`-f^{\prime}(-x)=f^{\prime}(x)`, chain rule,
...
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