anonymous
  • anonymous
Differentiate the given function: f(x)= ln (x+1)/(x-1) I get -2/(x-1)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
-2/ (x^2-1)
anonymous
  • anonymous
I used the quotient rule, but not sure what to do with the ln
anonymous
  • anonymous
did u have? ln(x+1/x-1)?

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anonymous
  • anonymous
if yes, then d/dx (lnx)= 1/x ... easy
anonymous
  • anonymous
the ln is before the fraction
anonymous
  • anonymous
Quotient rule u= ln (x+1) v= ln (x-1)
anonymous
  • anonymous
If ln is over the whole thing ln [(x+1)/(x-1)] rewrite as [ln (x+1)]/[ln (x-1)]
anonymous
  • anonymous
I don't know if this will help ln x+1 x-1 x+1/x-1 one big parenthesis around this fraction
anonymous
  • anonymous
Can be rewritten as \[\ln (x+1)\div \ln (x-1)\]
anonymous
  • anonymous
Top is u, bottom v
anonymous
  • anonymous
I have not done it that way
anonymous
  • anonymous
the u and v
anonymous
  • anonymous
what shorthand you use for quotient rule f(x) or what?
anonymous
  • anonymous
ok for quotient rule, I can do that but not sure what to do with the ln. After the quotient rule I get (x-1)-(x+1) / (x-1)^2
anonymous
  • anonymous
Excuse me for using u and v. Let u=ln (x+1), let v=ln (x-1) u'=?, v'=? u' means u prime or derivative of u The derivative of the whole thing is \[(u'v-uv')\div(v ^{2})\]
anonymous
  • anonymous
I am sorry but I am having a real hard time understanding this math. I have a book that has this problem worked out. I just don't understand why certain things are done the way they are. The last section we went over was dervatives and I did really well with them. These I am not.
anonymous
  • anonymous
OK, so write one or two steps from book and say what you don't understand
anonymous
  • anonymous
1st step f'(x) = 1/(x+1/x-1) d/dx (x+1/x-1) why did they put 1 over the problem.
anonymous
  • anonymous
next step x-1/x+1 [(x-1)(1) - (x+1)(1)//(x-1)^2 the 2nd half I get, that is the quotient rule
anonymous
  • anonymous
they are treating the whole fraction thingy as a single number. Let (x+1)/(x-1) be u (sorry) f' of ln u=1/u
anonymous
  • anonymous
Deal with one question at a time or everything would get confused
anonymous
  • anonymous
ok with step one 1/(x+1/x-1) then I guess they took the bottom # and flipped and multiplied. Is that how the problem got switched for step 2
anonymous
  • anonymous
OK, back to original question what might make it a little confusing is what is called chain rule. the f' (x) = 1/[x+1/(x-1)] du in addition to this you must find the derivative of the inner function (x+1)/(x-1). Find the derivative of that and that is your du. This is a complicated function. I can explain more after you look at it.
anonymous
  • anonymous
why can't I use the quotient rule
anonymous
  • anonymous
by putting the 1 / .... is that taking the ln out of the problem
anonymous
  • anonymous
There is a lot going on in this problem. It is not that you can't use quotient rule. In fact they are using quotient rule. But there are some intricacies that make their answer difficult to understand. Start from the top. Ask one piece by one piece what you don't understand.
anonymous
  • anonymous
ok 1st step 1/ (x+1/x-1) if I use the quotient rule derv. is x+1/x-1
anonymous
  • anonymous
never mind that isn't correct.
anonymous
  • anonymous
Just write the book line by line and I will do the play by play
anonymous
  • anonymous
1st step f'(x) = 1/(x+1/x-1) d/dx (x+1/x-1) 2nd step x-1/x+1 [(x-1)(1) - (x+1)(1)/(x-1)^2 step 3 -2/(x+1)(x-1) That is all steps
anonymous
  • anonymous
Are you familiar with the thing called the chain rule?
anonymous
  • anonymous
yes
anonymous
  • anonymous
There approach is good. Now that I see it. They considered the ln (that thing) ln (that thing)=[1/(that thing)][multiplied by derivative of that thing] They didn't find it necessary to do the quotient rule to find f'(x), but in finding the derivative of (that thing) they did the quotient rule. Derivative of ln doesn't require work, you just put 1/something
anonymous
  • anonymous
ok I half way understand that but how did they get x-1/x+1 in step 2 before the quotient rule
anonymous
  • anonymous
sometimes when they work the problems out in the book it doesn't explain what they are doing. If I understand the work it does not confuss me.
anonymous
  • anonymous
1/(B/C)=C/B
anonymous
  • anonymous
?
anonymous
  • anonymous
You have fractional property at the bottom is flipped.
anonymous
  • anonymous
ok you flip it to get rid of the 1
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok on step 2 x-1/x+1 [(x-1)(1)-(x+1)(1)/(x-1)^2 ok I can see the quotient rule what are they doine with the x-1/x+1, are they multipling that by the quotient?
anonymous
  • anonymous
never mind something just clicked, I see it now. They cross multiplied

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