If the derivative of a function f(x) is 1x^(-1), what is the derivative of 9f(x)?

If the derivative of a function f(x) is 1x^(-1), what is the derivative of 9f(x)?

$If\\ \frac{d}{dx}\;f(x)=\frac{1}{x}\\ then\\ \frac{d}{dx}\;[9f(x)]=\frac{9}{x}\\$

$\dfrac{d \;f(x)}{dx}=1x^{-1}\\ \dfrac{d}{dx} f(x)=\dfrac{1}{x}\\ f(x) = \int \dfrac{dx}{x}\\\quad\;\;\;\;\!=\ln|x|$

$\dfrac{d}{dx} 9\ln|x|=\dfrac{9}{x}$

Melody's way is a good way but I never knew this. Thanks Melody for presenting this method.