Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    i am stuck on this question:

    show that:

    tanh^-1(x)=1/2(ln(1+x/1-x))

    what i done was..

    x=tanhy

    dx/dy=sech^2y and so therefore dy/dx=1/sech^2y

    then using the identity: sech^y-1=tanh^2y

    i got: dy/dx=sech^2y-tanh^2y/tanh^2y+1

    but now i am stuck... any help please
    Offline

    18
    ReputationRep:
    It's an algebra problem - you shouldn't be differentiating. Instead:

    x = tanh y

    x = \dfrac{e^{2y}-1}{e^{2y} + 1}.

    Then, solve for y.

    You may find it useful to write Y = e^2y and solve for Y, then take logs to find y.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    Why are you differentiating?

    Express x = tanh y in terms of exponentials and change the subject.
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by DFranklin)
    It's an algebra problem - you shouldn't be differentiating. Instead:

    x = tanh y

    x = \dfrac{e^{2y}-1}{e^{2y} + 1}.

    Then, solve for y.

    You may find it useful to write Y = e^2y and solve for Y, then take logs to find y.
    ok so make x equal to the exponentials etc and then get Y and take log to work out what y equals to and i should end up with that answer... hmm i shall attempt it thank you
    • Thread Starter
    Offline

    12
    ReputationRep:
    did you mean by the way turn it into this then work out:

    x=y-1/y+1 ?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by sahil112)
    did you mean by the way turn it into this then work out:

    x=y-1/y+1 ?
    You are going to confuse yourself by using y to mean two different things. Anyway multiply both sides by y + 1, rearrange and factorise.
    • Thread Starter
    Offline

    12
    ReputationRep:
    ok i have ended up with y=-1-x/x-1

    i think i should sub x back into it now but dont no if that will make it very complicated?
    Offline

    13
    ReputationRep:
    (Original post by sahil112)
    ok i have ended up with y=-1-x/x-1

    i think i should sub x back into it now but dont no if that will make it very complicated?
    Y= x+1/1-x

    But Y=e^2y.

    So e^2y= x+1/1-x

    I guess you can do the rest?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 27, 2011

University open days

  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
  • Northumbria University
    All faculties Undergraduate
    Wed, 24 Oct '18
Poll
Who is most responsible for your success at university
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.