Math Help Forum

Math Help Forum Feed Site Feed

Go Back   Math Help Forum > University Math Help > Calculus
Reply
 
Thread Tools Display Modes
  #1  
Old September 18th, 2007, 04:43 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Question Derivative

I got the question f '(x) given:
f(x) = ln((8x+3)/(5x+8))

Now i first used quotient rule for inside bit and got:

(5x+8*8 - 8x+3*5) / (5x+8)^2

Now to use the chain rule for ln((8x+3)/(5x+8)) i am not sure, could someone help please?
Reply With Quote
Advertisement
 
  #2  
Old September 18th, 2007, 04:48 PM
Krizalid's Avatar
Math Engineering Student

 
Join Date: Mar 2007
Location: Santiago
Posts: 3,056
Country:
Thanks: 82
Thanked 1,362 Times in 1,086 Posts
Krizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant future
Send a message via MSN to Krizalid
Default

You better use

\ln\frac ab=\ln a-\ln b, for suitably a,b

Then take the derivative.
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  • Wanna type math symbols? You do need to download
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Got trouble with LaTeX?
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Make your partial integration (aka integration by parts) faster. Click
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to prove limits by the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to apply the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
Reply With Quote
  #3  
Old September 18th, 2007, 05:02 PM
Senior Member
 
Join Date: Apr 2006
Posts: 401
Country:
Thanks: 18
Thanked 128 Times in 124 Posts
AfterShock will become famous soon enoughAfterShock will become famous soon enough
Default

Quote:
Originally Posted by taurus View Post
I got the question f '(x) given:
f(x) = ln((8x+3)/(5x+8))

Now i first used quotient rule for inside bit and got:

(5x+8*8 - 8x+3*5) / (5x+8)^2

Now to use the chain rule for ln((8x+3)/(5x+8)) i am not sure, could someone help please?
There's a simple way to do it, but we'll do it your way.

If f(x) = \ln(\frac{8x + 3}{5x + 8}), then, f'(x) = \frac{1}{\frac{8x + 3}{5x + 8}} \cdot{derivative of inside here}

So, what is the derivative of the inside, that is, of:

\frac{8x + 3}{5x + 8}

Let's use the quotient rule.

\frac{8\cdot (5x + 8) - (8x + 3)\cdot 5}{(5x + 8)^2}

And thus, f'(x) = \frac{1}{\frac{8x + 3}{5x + 8}} \cdot \frac{8\cdot (5x + 8) - (8x + 3)\cdot 5}{(5x + 8)^2} = \frac{5x+8}{8x+3}\cdot \frac{8\cdot (5x + 8) - (8x + 3)\cdot 5}{(5x + 8)^2}

Note that 8\cdot (5x + 8) - (8x + 3)\cdot 5 = 49

\frac{5x+8}{8x+3}\cdot \frac{49}{(5x+8)^2} = \frac{49}{(5x+8)(8x+3)}
Reply With Quote
  #4  
Old September 18th, 2007, 05:03 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Question

alright yea i see, let me see if im right now:

--> ln(8x+3) - ln(5x+8)
--> 1/(8x+3) - 1/(5x+8)

(do i have to find the derivative of brackets, eg: 8x+3 => 8?)
Reply With Quote
  #5  
Old September 18th, 2007, 05:08 PM
Krizalid's Avatar
Math Engineering Student

 
Join Date: Mar 2007
Location: Santiago
Posts: 3,056
Country:
Thanks: 82
Thanked 1,362 Times in 1,086 Posts
Krizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant future
Send a message via MSN to Krizalid
Default

Uhhhmm, it's easier if we write f(x) as

f(x)=\ln(8x+3)-\ln(5x+8)\implies f'(x)=\frac8{8x+3}-\frac5{5x+8}
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  • Wanna type math symbols? You do need to download
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Got trouble with LaTeX?
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Make your partial integration (aka integration by parts) faster. Click
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to prove limits by the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to apply the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
Reply With Quote
The following users thank Krizalid for this useful post:
Donate to MHF
  #6  
Old September 18th, 2007, 05:12 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Default

Quote:
Originally Posted by Krizalid View Post
Uhhhmm, it's easier if we write f(x) as

f(x)=\ln(8x+3)-\ln(5x+8)\implies f'(x)=\frac8{8x+3}-\frac5{5x+8}
i thought lnx was 1/x?
Reply With Quote
  #7  
Old September 18th, 2007, 05:13 PM
Senior Member
 
Join Date: Apr 2006
Posts: 401
Country:
Thanks: 18
Thanked 128 Times in 124 Posts
AfterShock will become famous soon enoughAfterShock will become famous soon enough
Default

Quote:
Originally Posted by taurus View Post
i thought lnx was 1/x?
It is, but then you have to multiply by the "inside", and hence where the 5 and 8 come from.
Reply With Quote
  #8  
Old September 18th, 2007, 05:15 PM
Senior Member
 
Join Date: Apr 2006
Posts: 401
Country:
Thanks: 18
Thanked 128 Times in 124 Posts
AfterShock will become famous soon enoughAfterShock will become famous soon enough
Default

For example,

f(x) = \ln(5x) \Rightarrow f'(x) = \frac{1}{5x}\cdot 5 = \frac{1}{x}
Reply With Quote
  #9  
Old September 18th, 2007, 05:23 PM
Krizalid's Avatar
Math Engineering Student

 
Join Date: Mar 2007
Location: Santiago
Posts: 3,056
Country:
Thanks: 82
Thanked 1,362 Times in 1,086 Posts
Krizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant future
Send a message via MSN to Krizalid
Default

See The Chain Rule taurus.
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  • Wanna type math symbols? You do need to download
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Got trouble with LaTeX?
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Make your partial integration (aka integration by parts) faster. Click
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to prove limits by the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to apply the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
Reply With Quote
  #10  
Old September 18th, 2007, 05:25 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Default

Quote:
Originally Posted by AfterShock View Post
For example,

f(x) = \ln(5x) \Rightarrow f'(x) = \frac{1}{5x}\cdot 5 = \frac{1}{x}
wait so shoudlnt that be 5/5x, like the other one?
Reply With Quote
  #11  
Old September 18th, 2007, 05:28 PM
Senior Member
 
Join Date: Apr 2006
Posts: 401
Country:
Thanks: 18
Thanked 128 Times in 124 Posts
AfterShock will become famous soon enoughAfterShock will become famous soon enough
Default

Quote:
Originally Posted by taurus View Post
wait so shoudlnt that be 5/5x, like the other one?
And what is \frac{5}{5x}? Do you see that it's equal to \frac{1}{x}?
Reply With Quote
  #12  
Old September 18th, 2007, 06:18 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Default

Quote:
Originally Posted by AfterShock View Post
And what is \frac{5}{5x}? Do you see that it's equal to \frac{1}{x}?
ohhhh yea
Reply With Quote
  #13  
Old September 19th, 2007, 04:51 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Default

I got another question:
Find the simplest function g(q) such that

g'(q) = sin( 5 q) +cos( 5 q)

im not sure how i should go about solving it?
Reply With Quote
  #14  
Old September 19th, 2007, 05:11 PM
Krizalid's Avatar
Math Engineering Student

 
Join Date: Mar 2007
Location: Santiago
Posts: 3,056
Country:
Thanks: 82
Thanked 1,362 Times in 1,086 Posts
Krizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant futureKrizalid has a brilliant future
Send a message via MSN to Krizalid
Default

Well, you can integrate both sides to get g(q)
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  • Wanna type math symbols? You do need to download
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Got trouble with LaTeX?
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • Make your partial integration (aka integration by parts) faster. Click
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to prove limits by the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
  • How to apply the
    To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
    .
Reply With Quote
  #15  
Old September 19th, 2007, 05:18 PM
Member
 
Join Date: Sep 2007
Posts: 202
Country:
Thanks: 52
Thanked 1 Time in 1 Post
taurus is on a distinguished road
Default

what do you mean, how would i go about that?
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off
Forum Jump


All times are GMT -7. The time now is 03:58 PM.


Powered by vBulletin® Version 3.7.3
Copyright ©2000 - 2009, Jelsoft Enterprises Ltd.
SEO by vBSEO 3.2.0 ©2008, Crawlability, Inc.
©2005 - 2009 Math Help Forum


Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.