Question

Find the derivatives of the functions. f(x)=\frac{1}{\ln |x|}

Derivatives
ANSWERED
asked 2021-06-27
Find the derivatives of the functions. \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{\ln}{\left|{x}\right|}}}}\)

Answers (1)

2021-06-28
First, let's rewrite the function a bit.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{\ln}{\left|{x}\right|}}}}={\left({\ln}{\left|{x}\right|}\right)}^{{-{1}}}\)
Using the chain rule, we get
\(\displaystyle{f}'{\left({x}\right)}={\left[{\left({\ln}{\left|{x}\right|}\right)}^{{-{1}}}\right]}'=-{\left({\ln}{\left|{x}\right|}\right)}^{{-{2}}}{\left({\ln}{\left|{x}\right|}\right)}'\)
Recall that
\(\displaystyle{\left({\ln}{\left|{x}\right|}\right)}'={\frac{{{1}}}{{{x}}}}\)
Hence
\(\displaystyle{f}'{\left({x}\right)}=-{\left({\ln}{\left|{x}\right|}\right)}^{{-{2}}}{\frac{{{1}}}{{{2}}}}=-{\frac{{{1}}}{{{x}{\left({\ln}{\left|{x}\right|}\right\rbrace}^{{{2}}}}}}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...