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mathcalculus Group Title

HELP: Use your knowledge of the derivative to compute the limit given below: The derivative that is being calculated is

  • one year ago
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  1. mathcalculus Group Title
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    • one year ago
  2. mathcalculus Group Title
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    im confused. am i suppose to use the power rule or quotient rule to find the derivative?

    • one year ago
  3. asnaseer Group Title
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    do you know how to write the general form for the derivative of f(x)?

    • one year ago
  4. SithsAndGiggles Group Title
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    It sounds like the problem is asking you to recognize that the given limit is the definition of the derivative of some function. Given \(\displaystyle\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}\), find \(f(x)\). Then, simply compute the derivative.

    • one year ago
  5. asnaseer Group Title
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    ^

    • one year ago
  6. mathcalculus Group Title
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    yes

    • one year ago
  7. mathcalculus Group Title
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    im not sure how to start this

    • one year ago
  8. SithsAndGiggles Group Title
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    Well do you know how to find the derivative? The way the question is stated makes it sound like you've learned some of or all the "rules" for differentiation. In this case, since \(f(x)=\dfrac{1}{x^6}\), you would apply the power rule to find the derivative, and that would be your answer.

    • one year ago
  9. mathcalculus Group Title
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    right i used the power rule.

    • one year ago
  10. SithsAndGiggles Group Title
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    Okay, so that gives you \[f(x)=\frac{1}{x^6}=x^{-6}~\Rightarrow~f'(x)=\cdots\]

    • one year ago
  11. mathcalculus Group Title
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    -6/x^7

    • one year ago
  12. SithsAndGiggles Group Title
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    Right.

    • one year ago
  13. mathcalculus Group Title
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    ^_^

    • one year ago
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