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anonymous

  • 4 years ago

f(x)= ((6x)^−1/2) + 5 what is f ' (x)? if you use the power rule, please help me with the negative exponent, because I dont understand it

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  1. Rogue
    • 4 years ago
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    The power rule is as follows\[\frac {d}{dx} x^n = n x^{n-1}\]

  2. Rogue
    • 4 years ago
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    Is your function\[f(x) = 6x^{-.5} + 5\]or\[f(x) = (6x)^{-.5} + 5\]?

  3. anonymous
    • 4 years ago
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    the second one

  4. anonymous
    • 4 years ago
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    so it should be -.5(6x)^-3/2 should it not?

  5. Rogue
    • 4 years ago
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    If its the second one, then its not a variable to a power, but rather a function to a power. So the formula you must follow requires use of the chain rule, as well as the power rule.\[\frac {d}{dx} u^n = n u^{n-1} \frac {du}{dx}\]

  6. anonymous
    • 4 years ago
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    so what is the answer then?

  7. Rogue
    • 4 years ago
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    -3(6x)^(-3/2) I think

  8. Rogue
    • 4 years ago
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    You just have to multiply your answer that you have from the power rule by the derivative of u (6x), which is just 6.

  9. Rogue
    • 4 years ago
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    Actually, no, never mind, its still a variable to a power.

  10. Rogue
    • 4 years ago
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    Use the normal power rule.

  11. Rogue
    • 4 years ago
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    \[f(x) = \frac {x^{-.5}}{\sqrt {6}} + 5\]

  12. Rogue
    • 4 years ago
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    Gah, annoying powers...

  13. Rogue
    • 4 years ago
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    \[f'(x) = \frac {-1}{2} \frac {1}{\sqrt {6}} x^{-1.5} = \frac {-1}{2 \sqrt {6} x^{1.5}}\]

  14. anonymous
    • 4 years ago
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    try it the other way, it didnt wordk in the homework

  15. Rogue
    • 4 years ago
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    That last answer I gave should have been correct, unless its not the right problem... :( http://www.wolframalpha.com/input/?i=d%2Fdx+%286x%29^%28-.5%29+%2B+5

  16. anonymous
    • 4 years ago
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    the answer was 1/9

  17. Rogue
    • 4 years ago
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    Did they ask for f'(x) at a certain point?

  18. anonymous
    • 4 years ago
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    nevermind that was a different problem, but the other was still wrong kill me now!

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