Results 1 to 3 of 3

Math Help - How do you differentiate this function?!?

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    university
    Posts
    3

    How do you differentiate this function?!?

    f(x,y)= e^ax loge(y)


    I need to find the first order, second order and cross partial derivatives of this function. I have some answers that a friend has given me but I have no idea how they've been calculate what techniques/rules have been employed so any help/explanation would be greatly appreciated. Cheers!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,520
    Thanks
    1405

    Re: How do you differentiate this function?!?

    Quote Originally Posted by AEJD90 View Post
    f(x,y)= e^ax loge(y)


    I need to find the first order, second order and cross partial derivatives of this function. I have some answers that a friend has given me but I have no idea how they've been calculate what techniques/rules have been employed so any help/explanation would be greatly appreciated. Cheers!
    A general rule of thumb is that when performing a partial derivative, treat every variable except the variable being differentiated with respect to, as fixed or constant. The same derivative rules (such as the product, chain and quotient rules) still apply.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,603
    Thanks
    1421

    Re: How do you differentiate this function?!?

    First, the standard notation for "loge(y)" is ln(y). Do you know the derivative of ln(y) with respect to y? Do you know the derivative of e^{ax} with respect to x? As ProveIt said, to differentiate with respect to x, treat y as a constant, and to differentiate with respect to y, treat x as a constant. Here, you just have a function of x times a function of y: F(x, y)= f(x)g(y).

    So F_x= f_x(x)g(y), F_y= f(x)g_y(y), F_{xx}= f_{xx}(x)g(y), F_{yy}= f(x)g_{yy}(y), and F_{xy}= F_{yx}= f_x(x)g_y(y).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 20th 2012, 07:02 PM
  2. [SOLVED] Differentiate the following function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 12th 2011, 11:52 PM
  3. Differentiate a function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 16th 2010, 05:30 AM
  4. Replies: 2
    Last Post: June 5th 2009, 08:55 AM
  5. Replies: 3
    Last Post: May 25th 2009, 08:39 AM

Search Tags


/mathhelpforum @mathhelpforum