Question

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

f(x) = In3x^2

Answer 1

`(d(f(x)))/(dx) = (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:

`(d(\ln x))/(dx) = (1)/(x)\\\\(d(x^n))/(dx) = nx^(n-1)`

The derivation takes place in the following manner

`f(x) = \ln (3x^2)\\\\(d(f(x)))/(dx) = \displaystyle(d(\ln(3x^2)))/(dx)\\\\=(1)/(3x^2)* (d(3x^2))/(dx)\\\\= (1)/(3x^2)* (6x)\\\\=(6x)/(3x^2)\\\\=(2)/(x)`

`(d(f(x)))/(dx) = (2)/(x)`