0
The derivative of a constant is always 0. To show this, let's apply the definition of derivative.
Recall that the definition of derivative is:
f'(x) = lim h→0 (f(x + h) - f(x))/h
Let f(x) = 1. Then:
f'(x) = lim h→0 (1 - 1)/h
= lim h→0 0/h
= lim h→0 0
= 0!
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