(a) Definition of the even function:

If , then the function  is called even function.

Definition of the odd function :

If , then the function  is called odd function.

Consider .

Differentiate on each side with respect to .

.

From the definition of odd function it is to be said that  is an odd function.

Derivative of the even function is an odd function.

Consider an odd function .

.

Differentiate on each side with respect to .

.

From the definition of even function it is to be said that  is an even function.

Derivative of the odd function is an even function.

(a) Derivative of the even function is an odd function.

(b) Derivative of the odd function is an even function.