Find the derivatives of the functions. g(x)=\ln |3x−1|

sibuzwaW

sibuzwaW

Answered question

2021-09-20

Find the derivatives of the functions. \(\displaystyle{g{{\left({x}\right)}}}={\ln{

Answer & Explanation

Willie

Willie

Skilled2021-09-21Added 95 answers

Recall the generalized rule for the derivative of a natural logrithm of an absolute value:
ddx[ln|u|]=1ududx
In this exercise, we want to find the derivative of
g(x)=ln|3x1|
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)=1ududx=13x11dx(3x1)=33x1

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