## 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

1. anonymous

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

2. anonymous

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

3. anonymous

the second one

4. anonymous

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

5. anonymous

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

so what is the answer then?

7. anonymous

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

8. anonymous

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. anonymous

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

10. anonymous

Use the normal power rule.

11. anonymous

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

12. anonymous

Gah, annoying powers...

13. anonymous

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

14. anonymous

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

15. anonymous

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

17. anonymous

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

18. anonymous

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