find derivatives of real numbers?

Question

I don't understand why any real number, their derivative is zero.
according to the power rule, e.g: 2.
if i used the power rule

2^1 = 2
f'(x)= 1*2^(1-1)
f'(x)= 1
because anything to the zero would be one. Then why would real numbers equal zero? Unless I did my powerrule wrong.

Answer 1

most imp:
derivative is with respect to a variable
eg: x,y,etc.
therefore we always see their powers
this eg:
f(x)=2
f(x)=2x^0
f'(x)=0*2*x^(0-1)
f'(x)=0

Answer 2

the important thing to remember here is that a real number is a constant. constant means unchanging. when you take a derivative you are looking for the change and constants don't change, no change is zero change and that is why the derivative of a constant is 0. No matter what power , because 2^4 =16 and 16 does not =4(2^3).
Basically the change of a constant by definition is none=0.

Answer 3

If you are taking a derivative with respect to x, then you must realize that a constant will not affect the derivative. If you were to graph the derivative, the constant would not affect anything because it has no change. When you integrate this same derivative, the constant "c" can only change the location of the graph.The power rule pertains to powers of x.