Log differentitation

adam_dsutton · 2007-09-13 03:24:34

Hi, I'm struggling with the following questions.

1. Differentiate the following with respect to x: y=log(xe^x)

2. Find the derivatives of the following functions at the indicated points:

a) (cosx).log(3x) , x=pi

b) log((x^3)/(x^0.5)) , x=5/2

Any help is much appreciated as I havent a clue what to do here.
Thanks, Adam

luca-deltodesco · 2007-09-13 03:31:18

first of all, by log do you mean the natural logarithm (ln) or log base 10?

adam_dsutton · 2007-09-13 03:36:48

well i'm presuming log with base 10 but i dont actually know for sure, i just copied the questions exactly :S

Last edited by adam_dsutton (2007-09-13 03:37:29)

adam_dsutton · 2007-09-13 04:21:13

Okay, i've completed 2a) by substituting (ln) instead of log base 10, but I still can't get the correct answers for the other two questions.

luca-deltodesco · 2007-09-13 04:33:25

for 1 use product rule and chain rule

Last edited by luca-deltodesco (2007-09-13 04:48:19)

adam_dsutton · 2007-09-13 04:52:30

I understand everything apart from the first line...how do you know that f'(x)=1/(xlna) if f(x)=loga(x) ???
also the answers tell me that the answer is 1+(1/x) :S

thanks though luca, I hate to be a bother

luca-deltodesco · 2007-09-13 04:57:03

log((x^3)/(x^0.5))

x = 2.5

and conversly, using the logarithm equation again for logarithm of n'th base

luca-deltodesco · 2007-09-13 04:58:16

adam_dsutton wrote:

also the answers tell me that the answer is 1+(1/x)

then that tells me that the logarithm you are meant to be using is the natural logarithm NOT logarithm base 10

because then you'd have:

luca-deltodesco · 2007-09-13 05:00:43

so redoing my last two posts:

x = 2.5

adam_dsutton · 2007-09-13 05:02:04

Thankyou so much!

luca-deltodesco · 2007-09-13 05:06:02

for your question on my derivitive ill show you how i work it out:

first of all: prove the following:

then we have:

Last edited by luca-deltodesco (2007-09-13 05:07:36)

Math Is Fun Forum

#1 2007-09-13 03:24:34

Log differentitation

#2 2007-09-13 03:31:18

Re: Log differentitation

#3 2007-09-13 03:36:48

Re: Log differentitation

#4 2007-09-13 04:21:13

Re: Log differentitation

#5 2007-09-13 04:33:25

Re: Log differentitation

#6 2007-09-13 04:52:30

Re: Log differentitation

#7 2007-09-13 04:57:03

Re: Log differentitation

#8 2007-09-13 04:58:16

Re: Log differentitation

#9 2007-09-13 05:00:43

Re: Log differentitation

#10 2007-09-13 05:02:04

Re: Log differentitation

#11 2007-09-13 05:06:02

Re: Log differentitation

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