anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Rogue
  • Rogue
The power rule is as follows\[\frac {d}{dx} x^n = n x^{n-1}\]
Rogue
  • Rogue
Is your function\[f(x) = 6x^{-.5} + 5\]or\[f(x) = (6x)^{-.5} + 5\]?
anonymous
  • anonymous
the second one

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anonymous
  • anonymous
so it should be -.5(6x)^-3/2 should it not?
Rogue
  • Rogue
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.\[\frac {d}{dx} u^n = n u^{n-1} \frac {du}{dx}\]
anonymous
  • anonymous
so what is the answer then?
Rogue
  • Rogue
-3(6x)^(-3/2) I think
Rogue
  • Rogue
You just have to multiply your answer that you have from the power rule by the derivative of u (6x), which is just 6.
Rogue
  • Rogue
Actually, no, never mind, its still a variable to a power.
Rogue
  • Rogue
Use the normal power rule.
Rogue
  • Rogue
\[f(x) = \frac {x^{-.5}}{\sqrt {6}} + 5\]
Rogue
  • Rogue
Gah, annoying powers...
Rogue
  • Rogue
\[f'(x) = \frac {-1}{2} \frac {1}{\sqrt {6}} x^{-1.5} = \frac {-1}{2 \sqrt {6} x^{1.5}}\]
anonymous
  • anonymous
try it the other way, it didnt wordk in the homework
Rogue
  • Rogue
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
anonymous
  • anonymous
the answer was 1/9
Rogue
  • Rogue
Did they ask for f'(x) at a certain point?
anonymous
  • anonymous
nevermind that was a different problem, but the other was still wrong kill me now!

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