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Proof of the Derivative of a Constant: d(c)/dx = 0
It is very easy to prove by using the definition of the derivative therefore define, f(x) = c and the utilize the definition of the derivative.
f'(x) = limh→0 (f(x +h) - f(x))/h
= limh→0 (c - c)/h
= limh→0 0 = 0
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