# Why is derivative of constant zero?

##### 3 Answers

The derivative represents the change of a function at any given time.

Take and graph the constant

graph{0x+4 [-9.67, 10.33, -2.4, 7.6]}

The constant never changes—it is *constant*.

Thus, the derivative will always be

Consider the function

graph{x^2-3 [-9.46, 10.54, -5.12, 4.88]}

It is the same as the function

graph{x^2 [-9.46, 10.54, -5.12, 4.88]}

The functions increase at exactly the same rate, just in a slightly different location.

Thus, their derivatives are the same—both *changes*.

Use the power rule:

A constant, say

Thus, according to the power rule, the derivative of

which equals

Since any constant can be written in terms of

Use the limit definition of the derivative:

If

Thus,