Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    http://www.thestudentroom.co.uk/show....php?t=2705197

    For the S14 IAL F2 Model answers found in the above thread,

    for question 5 part a,

    can someone tell me how arsey goes from 2xy''' to 2x(2xy" )
    Offline

    22
    ReputationRep:
    (Original post by Katiee224)
    http://www.thestudentroom.co.uk/show....php?t=2705197

    For the S14 IAL F2 Model answers found in the above thread,

    for question 5 part a,

    can someone tell me how arsey goes from 2xy''' to 2x(2xy" )
    He's differentiating 2xy''' using the product rule.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Zacken)
    He's differentiating 2xy''' using the product rule.
    but when you differentiate 2xy''' you get 2xy'''' + 2y''' ?
    Offline

    22
    ReputationRep:
    (Original post by Katiee224)
    but when you differentiate 2xy''' you get 2xy'''' + 2y''' ?
    Aye, sorry - we have y^{(3)} = 2xy^{(2)} (y^{(3)} means the third derivative of y) differentiating this using the product rule we get: y^{(4)} = 2xy^{(3)} + 2y^{(2)}

    But we know something about y^(3), i.e: that it is the same thing as y^{(3)} = 2xy^{(2)} so we can just replace it into our y^{(4)}, so that:

    \displaystyle

\begin{equation*}y^{(4)} = 2xy^{(3)} + 2y^{(2)} = 2x(2xy^{(2)}) + 2y^{(2)}\end{equation*}
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Zacken)
    Aye, sorry - we have y^{(3)} = 2xy^{(2)} (y^{(3)} means the third derivative of y) differentiating this using the product rule we get: y^{(4)} = 2xy^{(3)} + 2y^{(2)}

    But we know something about y^(3), i.e: that it is the same thing as y^{(3)} = 2xy^{(2)} so we can just replace it into our y^{(4)}, so that:

    \displaystyle

\begin{equation*}y^{(4)} = 2xy^{(3)} + 2y^{(2)} = 2x(2xy^{(2)}) + 2y^{(2)}\end{equation*}
    At the risk of sounding stupid here... why does y^{(3)} = 2xy^{(2)} ?
    Offline

    22
    ReputationRep:
    (Original post by Katiee224)
    At the risk of sounding stupid here... why does y^{(3)} = 2xy^{(2)} ?
    The question gives us y'' -2xy'  + 2y = 0 differentiating this:

    \displaystyle

 \begin{equation*}y^{(3)} - 2xy''  - 2y' + 2y' = 0 \iff y^{(3)} = 2xy''\end{equation*}

    by using the product rule on the middle term and re-arranging.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Zacken)
    The question gives us y'' -2xy'  + 2y = 0 differentiating this:

    \displaystyle

 \begin{equation*}y^{(3)} - 2xy''  - 2y' + 2y' = 0 \iff y^{(3)} = 2xy''\end{equation*}

    by using the product rule on the middle term and re-arranging.
    ohhh they simply got that from the first part of the working and substituted it in to the second

    haha i feel super dumb for not spotting that, appreciate the help
    Offline

    22
    ReputationRep:
    (Original post by Katiee224)
    ohhh they simply got that from the first part of the working and substituted it in to the second

    haha i feel super dumb for not spotting that, appreciate the help
    No problem.
 
 
 
Poll
Who is your favourite TV detective?
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

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.