Results 1 to 6 of 6

Math Help - Logarithmic Differentiation Question

  1. #1
    Junior Member
    Joined
    Nov 2006
    Posts
    38

    Logarithmic Differentiation Question

    I am having trouble with this questoin...

    Find the slope (exact value) of the normal to the curve xe^y + ylnx = 2 at the point (1, ln2).

    Thanks for any help!
    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 ty2391 View Post
    I am having trouble with this questoin...

    Find the slope (exact value) of the normal to the curve xe^y + ylnx = 2 at the point (1, ln2).

    Thanks for any help!
    Differentiate both sides of x e^y + y \ln x = 2 with respect to x, using the product rule as required:


    e^y + x \left( e^y \frac{dy}{dx} \right) + \frac{dy}{dx} \ln x + \frac{y}{x} = 0.


    Note: From the chain rule, the derivative with respect to x of e^y is \frac{d}{dy}\left[ e^y \right] \frac{dy}{dx} = e^y \frac{dy}{dx}.


    Now substitute x = 1 and y = ln 2. Note: e^{\ln 2} = 2.

    Now solve for \frac{dy}{dx}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2006
    Posts
    38
    I ended up with:

    2 / ln 2 + 2

    as my answer...

    Can someone confirm this?
    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 ty2391 View Post
    I ended up with:

    2 / ln 2 + 2

    as my answer...

    Can someone confirm this?
    e^y + x \left( e^y \frac{dy}{dx} \right) + \frac{dy}{dx} \ln x + \frac{y}{x} = 0.

    Substitute x = 1 and y = ln 2:

    2 + 2 \frac{dy}{dx} + \ln 2 = 0 \Rightarrow \frac{dy}{dx} = -\frac{(2 + \ln 2)}{2} ....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2006
    Posts
    38
    It's looking for the normal though, so I guess I am right?
    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 ty2391 View Post
    It's looking for the normal though, so I guess I am right?
    (My boldface). After what I posted, you need to guess!?
    Last edited by mr fantastic; February 22nd 2008 at 01:24 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Logarithmic Differentiation?
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 5th 2011, 08:56 PM
  2. [SOLVED] Logarithmic Differentiation Question
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 1st 2011, 12:54 PM
  3. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 14th 2010, 01:41 AM
  4. Logarithmic Differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 13th 2009, 12:25 PM
  5. Logarithmic Differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 13th 2008, 02:56 AM

Search Tags


/mathhelpforum @mathhelpforum