anonymous
  • anonymous
relative rate of change for f(x)= 5x - xlnx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Same deal as before. From the definition,\[\frac{f'(x)}{f(x)}=\frac{5-(\ln x+1)}{5x-x \ln x}=\frac{4-\ln x}{x(5-\ln x)}\]
anonymous
  • anonymous
Are you having trouble with taking the derivative?
anonymous
  • anonymous
yeah i wasnt sure how to get the derivative.

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anonymous
  • anonymous
jsut when you have ln
anonymous
  • anonymous
I'm thinking it's the xlnx bit?
anonymous
  • anonymous
\[\frac{d}{dx}x \ln x=x \frac{d}{dx}\ln x+\ln x \frac{d}{dx}x=x \times \frac{1}{x}+\ln x \times 1\]\[=1+\ln x\]
anonymous
  • anonymous
So the entire derivative in the numerator is\[f'(x)=5-(1+\ln x)=4-\ln x\]
anonymous
  • anonymous
thanks
anonymous
  • anonymous
no worries
anonymous
  • anonymous
im trying to correct this test and this class is killing me
anonymous
  • anonymous
we'll do our best to help
anonymous
  • anonymous
Thanks
anonymous
  • anonymous
Thanks

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