Derivative of a Number

The simplest answer to the question "What is the derivative of a number?" is straightforward: the derivative of a number is zero.

Understanding the Derivative

Let's recall the meaning of the derivative. It shows the rate of change of the value of a function relative to the change of its argument.
In simpler terms, the derivative measures how a function's output changes as its input changes.

Derivative of a Constant Function

For example, let's find the derivative of the number three. Visually, you can imagine this not as (3)', but as the need to find
the derivative of the function f(x)=3.

In this case, for any change in the argument of the function x, the value of the function does not change. 

The function f(x)=3 is a constant function, meaning its value is always three, regardless of the value of x.

Rate of Change

What is the rate of change of the value of the function in this case? It is zero. 

No matter how much the argument of the function changes, the value of the function f(x)=3 will always equal three.
There is no change in the value of the function.

The same logic applies to any constant function f(x)=c, where c is a constant number. 
The derivative of a constant function is always zero.

Conclusion

From this, we can conclude:

• The derivative of a constant number is zero.