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

Derivative of even function is

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

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

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

Derivative of odd function is

Prove that the product of two even or two odd functions is an even function, whereas the product of an even and an odd function is an odd function.