Answer:
[tex]\dfrac{d(f(x))}{dx} = \dfrac{2}{x}[/tex]
Step-by-step explanation:
We are given the following function in the question:
[tex]f(x) = \ln (3x^2)[/tex]
We have to derivate the given function.
Formula:
[tex]\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}[/tex]
The derivation takes place in the following manner
[tex]f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}[/tex]
[tex]\dfrac{d(f(x))}{dx} = \dfrac{2}{x}[/tex]
