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anonymous

  • 5 years ago

relative rate of change for f(x)= 5x - xlnx

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  1. anonymous
    • 5 years ago
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    Same deal as before. From the definition,\[\frac{f'(x)}{f(x)}=\frac{5-(\ln x+1)}{5x-x \ln x}=\frac{4-\ln x}{x(5-\ln x)}\]

  2. anonymous
    • 5 years ago
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    Are you having trouble with taking the derivative?

  3. anonymous
    • 5 years ago
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    yeah i wasnt sure how to get the derivative.

  4. anonymous
    • 5 years ago
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    jsut when you have ln

  5. anonymous
    • 5 years ago
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    I'm thinking it's the xlnx bit?

  6. anonymous
    • 5 years ago
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    \[\frac{d}{dx}x \ln x=x \frac{d}{dx}\ln x+\ln x \frac{d}{dx}x=x \times \frac{1}{x}+\ln x \times 1\]\[=1+\ln x\]

  7. anonymous
    • 5 years ago
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    So the entire derivative in the numerator is\[f'(x)=5-(1+\ln x)=4-\ln x\]

  8. anonymous
    • 5 years ago
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    thanks

  9. anonymous
    • 5 years ago
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    no worries

  10. anonymous
    • 5 years ago
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    im trying to correct this test and this class is killing me

  11. anonymous
    • 5 years ago
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    we'll do our best to help

  12. anonymous
    • 5 years ago
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    Thanks

  13. anonymous
    • 5 years ago
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    Thanks

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