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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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Derivative of even function is

The derivative of an even function is always an odd function.

Prove that the derivative of (a) an odd function is an even function;

If f is an even function and g is an odd function then the function fog is

Statement -1 : Integral of an even function is not always on odd function. Statement-2: Integral of an odd function is an even function.

Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

Derivative of odd function is