Question: "Find the derivatives of the functions. g(x)=ln∣3x−1∣"

Isa Trevino

Answered question

2021-05-23

Find the derivatives of the functions. $g (x) = \ln ∣ 3 x - 1 ∣$

Cristiano Sears

Skilled2021-05-24Added 96 answers

Recall the generalized rule for the derivative of a natural logrithm of an absolute value:

\frac{d}{d x} [\ln | u |] = \frac{1}{u} \frac{d u}{d x}

In this exercise, we want to find the derivative of

g (x) = \ln | 3 x - 1 |

To make use of the rule in Step 1, denote the expression inside the absolute value by u, i.e.
u=3x-1
Using the above-mentioned rule, we get

g^{'} (x) = \frac{1}{u} \frac{d u}{d x} = \frac{1}{3 x - 1} \frac{1}{d x} (3 x - 1) = \frac{3}{3 x - 1}

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