proof of constant times a function cfxprime cf

Question

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))′ = lim_h→0 (cf(x + h) - cf(x))/h

= c lim_h→0 (f(x + h) - f(x))/h

= cf'(x)