Log differentiation examples!

  • Thread starter A_Munk3y
  • Start date
  • #1
72
0

Homework Statement



Hi again
Practicing log differentiation now :P

Sorry for all the questions, i have a midterm on thursday and i need to get this stuff by then

1. ex2ln(2x+1)
2.ln(2x/(2x+1))
3. (3x-2)x (use logarithmic differentiation even though unnecessary




The Attempt at a Solution


1. ex2ln(2x+1)
=>ex2*2x*(2/(2x+1))
is that right?

2. ln(2x/(2x+1))
=>ln(2x)-ln(2x+1)
=>2/(2x)-2(2x+1)
and is that one right? :)

3. (3x-2)x
f(x)=(3x-2)x
ln(y)=ln[((3x-2)x]
=>ln(y)=xln(3x-2)
=>1/y*y'=1*1/(3x-2)*3
=>1/y*y'=3/(3x-2)
=>y'=y(3/(3x-2)
=>y'=(3x-2)x(3/(3x-2)
 
Last edited:

Answers and Replies

  • #2
Mentallic
Homework Helper
3,798
94
You've forgotten how to use the product rule.

[tex]y'=u'v+v'u[/tex]

Where u and v are some functions of x.

1) let [tex]u=e^{x^2}[/tex] and [tex]v=ln(2x+1)[/tex]

2) assuming you meant 2/(2x+1) then yes it's right. By the way, it's nice to see that you converted the log(a/b) into log(a)-log(b) first and then took the derivative. This is a much faster way than taking the derivative of the quotient, not to mention less prone to mistake.

3) For xln(3x-2) use the product rule.
 
  • #3
72
0
wow :( that's embarassing lol

so is it right now?
1. 1. ex2ln(2x+1)
=>ex2*2/(2x+1)+ln(2x+1)*ex2*2x


3. (3x-2)x
f(x)=(3x-2)x
ln(y)=ln[((3x-2)x]
=>ln(y)=xln(3x-2)
=>1/y*y'=x*1/(3x-2)*3+ln(3x-2)*1
=>1/y*y'=3/(3x-2)+ln(3x-2)
=>y'=y[(3/(3x-2))+ln(3x-2)]
=>y'=(3x-2)x[3/(3x-2)+ln(3x-2]
??
hopefully lol, this is so much confusion!!
 
  • #4
Mentallic
Homework Helper
3,798
94
Yes you got it right :smile:

=>1/y*y'=x*1/(3x-2)*3+ln(3x-2)*1
=>1/y*y'=3/(3x-2)+ln(3x-2)

You accidentally got rid of the x between these two lines. 3/(3x-2) should be 3x/(3x-2).
 
  • #5
72
0
:D
Yup, didn't pay attention to that.
Ok, thank you so much for all the help mate :)
I really appreciate it
 
  • #6
Mentallic
Homework Helper
3,798
94
No worries. Good luck!
 

Related Threads on Log differentiation examples!

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
512
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
874
  • Last Post
Replies
2
Views
1K
Replies
4
Views
996
Replies
3
Views
1K
Replies
1
Views
2K
Replies
14
Views
2K
  • Last Post
Replies
2
Views
1K
Top