Question

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

Answer 1

Answer:

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$

Step-by-step explanation:  

We are given the following function in the question:

$f(x) = \ln (3x^2)$

We have to derivate the given function.

Formula:

$\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}$

The derivation takes place in the following manner

$f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}$

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$