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Proof of Constant Times a Function: (cf(x))′ = cf ′(x)
It is very easy property to prove using the definition given you a recall, we can factor a constant out of a limit. Now there is the work for this property.
(cf(x))′ = limh→0 (cf(x + h) - cf(x))/h
= c limh→0 (f(x + h) - f(x))/h
= cf'(x)
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