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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
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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Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0The power rule is as follows\[\frac {d}{dx} x^n = n x^{n1}\]

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0Is your function\[f(x) = 6x^{.5} + 5\]or\[f(x) = (6x)^{.5} + 5\]?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so it should be .5(6x)^3/2 should it not?

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0If 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.\[\frac {d}{dx} u^n = n u^{n1} \frac {du}{dx}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what is the answer then?

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0You just have to multiply your answer that you have from the power rule by the derivative of u (6x), which is just 6.

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0Actually, no, never mind, its still a variable to a power.

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0Use the normal power rule.

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = \frac {x^{.5}}{\sqrt {6}} + 5\]

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0\[f'(x) = \frac {1}{2} \frac {1}{\sqrt {6}} x^{1.5} = \frac {1}{2 \sqrt {6} x^{1.5}}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0try it the other way, it didnt wordk in the homework

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0That 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

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0Did they ask for f'(x) at a certain point?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0nevermind that was a different problem, but the other was still wrong kill me now!
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