im stuck here, how do i do this?

g(x) = ( log [10] x ) / (x^2)

note:

log [10] x-- this is log, sub 10, x... i didnt know how to write it out

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- Aug 30th 2007, 09:04 PMrunner07Bases other than e... help?
im stuck here, how do i do this?

g(x) = ( log [10] x ) / (x^2)

note:

log [10] x-- this is log, sub 10, x... i didnt know how to write it out - Aug 30th 2007, 09:05 PMJhevon
- Aug 30th 2007, 09:13 PMrunner07
ahh sorry, it says to differentiate the function.

- Aug 30th 2007, 09:20 PMJhevon
- Aug 30th 2007, 09:25 PMrunner07
- Aug 30th 2007, 09:27 PMJhevon
- Aug 30th 2007, 09:40 PMrunner07
oh wait, so would i get the derivative of lnx/ln10 first then plug it into that?

- Aug 30th 2007, 09:43 PMJhevon
- Aug 30th 2007, 09:48 PMrunner07
- Aug 30th 2007, 10:21 PMearboth
- Aug 31st 2007, 04:52 AMJhevon
as earboth already said, when we have a constant multiplier to a derivative, we can essentially forget about it and differentiate the (variable) function and then apply the constant multiplier when we're done. in fact, this is one of the properties of derivatives:

where is a constant - Aug 31st 2007, 07:19 AMSoroban
Hello, runner07!

You should have been shown the formula for "other bases".

Quote:

im stuck here, how do i differentiate this?

. .

*derive*the formula . . . (Yeah, right!)

We have: . . ... where is a positive real number

. . Re-write in exponential form: .

. . Take logs: .

. . Differentiate implicitly: .

Therefore: .

So the derivative of is: .

- Aug 31st 2007, 07:48 AMKrizalid
You can use the product rule too :)

So, all we have to do it's take the derivative of , now by the product rule