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

Question

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

rogue · Answer

The power rule is as follows$$\frac {d}{dx} x^n = n x^{n-1}$$

rogue · Answer

Is your function$$f(x) = 6x^{-.5} + 5$$or$$f(x) = (6x)^{-.5} + 5$$?

anonymous · Answer

the second one

anonymous · Answer

so it should be -.5(6x)^-3/2 should it not?

rogue · Answer

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 · Answer

so what is the answer then?

rogue · Answer

-3(6x)^(-3/2) I think

rogue · Answer

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 · Answer

Actually, no, never mind, its still a variable to a power.

rogue · Answer

Use the normal power rule.

rogue · Answer

$$f(x) = \frac {x^{-.5}}{\sqrt {6}} + 5$$

rogue · Answer

Gah, annoying powers...

rogue · Answer

$$f'(x) = \frac {-1}{2} \frac {1}{\sqrt {6}} x^{-1.5} = \frac {-1}{2 \sqrt {6} x^{1.5}}$$

anonymous · Answer

try it the other way, it didnt wordk in the homework

rogue · Answer

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 · Answer

the answer was 1/9

rogue · Answer

Did they ask for f'(x) at a certain point?

anonymous · Answer

nevermind that was a different problem, but the other was still wrong kill me now!