Derivative of the product of a function by a constant (possible typo)

[mcastillo356]

TL;DR

I think there is a typo in this demo

Hi, PF, I think I've found a typo in my textbook. It says:

"In the case of a multiplication by a constant, we've got

$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$"

My opinion: it should be

$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=C\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$

Greetings!

 

[PeroK]

definitely a typo.