Results 1 to 6 of 6

Math Help - Help with to derive this

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    4

    Help with to derive this

    Hi Guys,

    this may seem like a very simple question to some of you.. but im struggling.. could someone please help me derive this:

    f(x,y) = ln(x-3y)

    Chain rule?.. if so ive confused myself with the x's and the y's

    basicly ive been asked to find the linear approximation of that function at (7,2) and then use it to approximate f(6.9, 2.06).. could someone please confim the below process?

    Find f(7,2)

    Find f ′(x,y)

    Find f ′(7,2)

    Use formula for linear approximation near the point a .... f(x) ≈ f(a) + f ′(a) (x - a) not sure about this part.. what happened to the y's?


    Substitute a = 7

    then im unsure...

    any help would be much appricated :-)
    Last edited by DoesNotCompute; August 13th 2010 at 04:10 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DoesNotCompute View Post
    Hi Guys,

    this may seem like a very simple question to some of you.. but im struggling.. could someone please help me derive this:

    f(x,y) = ln(x-3y)

    Chain rule?.. if so ive confused myself with the x's and the y's

    basicly ive been asked to find the linear approximation of that function at (7,2) and then use it to approximate f(6.9, 2.06).. could someone please confim the below process?

    Find f(7,2)

    Find f ′(x,y)

    Find f ′(7,2)

    Use formula for linear approximation near the point a .... f(x) ≈ f(a) + f ′(a) (x - a) not sure about this part.. what happened to the y's?


    Substitute a = 7

    then im unsure...

    any help would be much appricated :-)
    Do you know how to differentiate ln(x-a) wrt x? Do you know how to differentiate ln(b-3y) wrt y?

    (You ought to if you're studying multivariable calculus. If you don't, then the question you have posted is not your immediate problem. Your immediate problem would be to urgently review all of the pre-requisite single variable calculus that your instructor will assume you already know).

    Then you know how to calculate the partial derivatives f_x and f_y.

    Your linear approximation formula is the wrong one to use for this question. You have quoted the single variable formula. The formula required is the two variable formula. It will be in your classnotes or textbook. I suggest you find it (and then review all the examples that will follow it).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2010
    Posts
    4
    Quote Originally Posted by mr fantastic View Post
    Do you know how to differentiate ln(x-a) wrt x? Do you know how to differentiate ln(b-3y) wrt y?

    (You ought to if you're studying multivariable calculus. If you don't, then the question you have posted is not your immediate problem. Your immediate problem would be to urgently review all of the pre-requisite single variable calculus that your instructor will assume you already know).

    Then you know how to calculate the partial derivatives f_x and f_y.

    Your linear approximation formula is the wrong one to use for this question. You have quoted the single variable formula. The formula required is the two variable formula. It will be in your classnotes or textbook. I suggest you find it (and then review all the examples that will follow it).
    Hi There,

    thanks for your reply,

    you are correct in saying i have major gaps in my understanding of single variable and well as mutli. taking your advice i have looked through the book and its starting to make abit more sence now.. but im still confused as to how i differentiate the function... this is my delima =>

    do i use:

    dy/dx = dy/du . du/dx

    so by chain rule

    dy/du = -3/(x-3y) and du/dx = 1/(x-3y) so dy/dx = -3/(x-3y)

    or

    dx/dt = ∂f/∂x . dx/dt + ∂f/∂y . dy/dt ? ... what is "t"?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DoesNotCompute View Post
    Hi There,

    thanks for your reply,

    you are correct in saying i have major gaps in my understanding of single variable and well as mutli. taking your advice i have looked through the book and its starting to make abit more sence now.. but im still confused as to how i differentiate the function... this is my delima =>

    do i use:

    dy/dx = dy/du . du/dx

    so by chain rule

    dy/du = -3/(x-3y) and du/dx = 1/(x-3y) so dy/dx = -3/(x-3y)

    or

    dx/dt = ∂f/∂x . dx/dt + ∂f/∂y . dy/dt ? ... what is "t"?
    By the chain rule, \frac{d}{dx} \ln (ax + b) = \frac{a}{ax + b}. It can equally be said that \frac{d}{dy} \ln (ay + b) = \frac{a}{ay + b}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2010
    Posts
    4
    thanks for your help again.. im sorry.. but im still confused:

    chain rule: f'(x) = f '(g(x)) g '(x) so

    f '(x) = 1/(x-3y) . 1
    => 1/(x-3y)

    and then

    f '(y) = 1/(x-3y) . -3
    => -3/(x-3y)

    is this correct for the partial derivatives?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DoesNotCompute View Post
    thanks for your help again.. im sorry.. but im still confused:

    chain rule: f'(x) = f '(g(x)) g '(x) so

    f '(x) = 1/(x-3y) . 1
    => 1/(x-3y)

    and then

    f '(y) = 1/(x-3y) . -3
    => -3/(x-3y)

    is this correct for the partial derivatives?
    Overlooking the poor notation, your answers for the partial derivatives are correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 27th 2011, 08:19 AM
  2. Derive tan (x/2)
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 25th 2010, 12:51 AM
  3. Please help me derive this!!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 15th 2009, 06:46 PM
  4. Derive 6 help please
    Posted in the Math Software Forum
    Replies: 0
    Last Post: April 8th 2009, 05:00 PM
  5. derive
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 29th 2009, 09:42 PM

Search Tags


/mathhelpforum @mathhelpforum