Results 1 to 7 of 7

Math Help - Partial Derivatives

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    20

    Partial Derivatives

    Suppose f is a differentiable function of x and y, and g(u,v)=f(e^u+sinv, e^u+cosv) use the table of values to calculate gu(0,0) and gv(0,0).

    at (0,0) f=3, g=6 fx=4 fx=8

    I have no clue how to do this someone please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,325
    Thanks
    10
    Quote Originally Posted by multivariablecalc View Post
    Suppose f is a differentiable function of x and y, and g(u,v)=f(e^u+sinv, e^u+cosv) use the table of values to calculate gu(0,0) and gv(0,0).

    at (0,0) f=3, g=6 fx=4 fx=8

    I have no clue how to do this someone please help
    Let x = e^u+\sin v and y = e^u+\cos v so

     <br />
g_u = f_x x_u + f_y y_u = e^u f_x + e^u f_y<br />
     <br />
g_v = f_x x_v + f_y y_v = \cos v f_x - \sin v f_y<br />

    Do you have a table of values for f_x(1,2) and f_y(1,2)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    If the problem say "use the table of values" you had better have a table of values! Please post the entire problem, including the table of values.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2011
    Posts
    26
    fx(1,2)=2, fy(1,2)=5, f(0,0)=3, f(1,2)=6, g(0,0)=6, g(1,2)=3, fx(0,0)=4,fy(0,0)=8
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Welcome back! Do you see why you needed to know fx(1,2) and fy(1,2)?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2011
    Posts
    26
    Well I am not the same person who posted this thread. However, assuming this person was referring to problem #11 of section 11.5 of Essential Calculus-Early Transcendentals (James Stewart), then these are the correct values. If I am not mistaken, gu(0,0)=fx(1,2)e^u +fy(1,2)e^u =2e^0 +5e^0=7. gv(0,0) is not much different.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Oh, I see! (Although if you had gone on a 4-month quest for the table of values perhaps you would have have returned a different person!)

    I don't think you're mistaken. Hopefully you can also see how Danny was holding one variable constant while differentiating with respect to the other.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Partial Derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2011, 05:07 PM
  2. Partial derivatives
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 9th 2009, 09:31 AM
  3. Partial Derivatives....help!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 9th 2008, 02:44 PM
  4. Partial Derivatives...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 30th 2007, 07:00 PM
  5. Partial derivatives
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 6th 2007, 07:22 PM

Search Tags


/mathhelpforum @mathhelpforum