anonymous
  • anonymous
Use logarithmic differentiation to find the derivative of the function:
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
start with \[\ln(y)=\frac{1}{6}(\ln(x^2+1)-\ln(x+1)-\ln(x-1))\] then take the derivative term by term
anonymous
  • anonymous
\[\frac{1}{6}\left (\frac{2x}{(x^2+1)}-\frac{1}{x+1}-\frac{1}{x-1}\right )\]

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anonymous
  • anonymous
then multiply by the original function and you are done
anonymous
  • anonymous
Why multiply by the original?
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anonymous
  • anonymous
oh because you are taking the log as the first step
anonymous
  • anonymous
\[\frac{d}{dx}\left[\ln(f(x))\right]=\frac{f'(x)}{f(x)}\iff f'(x)=f(x)\times \frac{d}{dx}\left[\ln(f(x))\right ]\]
anonymous
  • anonymous
anonymous
  • anonymous

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