Question

Differentiate the given function:

f(x)= ln (x+1)/(x-1)

I get -2/(x-1)^2

Answer 1

-2/ (x^2-1)

Answer 2

I used the quotient rule, but not sure what to do with the ln

Answer 3

did u have? ln(x+1/x-1)?

Answer 4

if yes, then d/dx (lnx)= 1/x ... easy

Answer 5

the ln is before the fraction

Answer 6

Quotient rule
u= ln (x+1)
v= ln (x-1)

Answer 7

If ln is over the whole thing ln [(x+1)/(x-1)]
rewrite as [ln (x+1)]/[ln (x-1)]

Answer 8

I don't know if this will help

ln x+1
x-1


x+1/x-1 one big parenthesis around this fraction

Answer 9

Can be rewritten as \[\ln (x+1)\div \ln (x-1)\]

Answer 10

Top is u, bottom v

Answer 11

I have not done it that way

Answer 12

the u and v

Answer 13

what shorthand you use for quotient rule f(x) or what?

Answer 14

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

Answer 15

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 \[(u'v-uv')\div(v ^{2})\]

Answer 16

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.

Answer 17

OK, so write one or two steps from book and say what you don't understand

Answer 18

1st step

f'(x) = 1/(x+1/x-1) d/dx (x+1/x-1)

why did they put 1 over the problem.

Answer 19

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

Answer 20

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

Answer 21

Deal with one question at a time or everything would get confused

Answer 22

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

Answer 23

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.

Answer 24

why can't I use the quotient rule

Answer 25

by putting the 1 / .... is that taking the ln out of the problem

Answer 26

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.

Answer 27

ok 1st step 1/ (x+1/x-1)
if I use the quotient rule derv. is x+1/x-1

Answer 28

never mind that isn't correct.

Answer 29

Just write the book line by line and I will do the play by play

Answer 30

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

Answer 31

Are you familiar with the thing called the chain rule?

Answer 32

yes

Answer 33

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

Answer 34

ok I half way understand that but how did they get x-1/x+1 in step 2 before the quotient rule

Answer 35

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.

Answer 36

1/(B/C)=C/B

Answer 37

?

Answer 38

You have fractional property at the bottom is flipped.

Answer 39

ok you flip it to get rid of the 1

Answer 40

yes

Answer 41

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?

Answer 42

never mind something just clicked, I see it now. They cross multiplied