Results 1 to 4 of 4

Thread: implicit differentiation problem

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    98

    implicit differentiation problem

    If and , find by implicit differentiation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by tbenne3 View Post
    If and , find by implicit differentiation.
    $\displaystyle \frac{1}{x} + \frac{1}{y} = 2$

    $\displaystyle x^{-1} + y^{-1} = 2$

    $\displaystyle \frac{d}{dx}(x^{-1} + y^{-1}) = \frac{d}{dx}(2)$

    $\displaystyle -x^{-2} + \frac{d}{dy}(y^{-1})\,\frac{dy}{dx} = 0$

    $\displaystyle -\frac{1}{x^2} - \frac{1}{y^2}\,\frac{dy}{dx} = 0$

    $\displaystyle -\frac{1}{y^2}\,\frac{dy}{dx} = \frac{1}{x^2}$

    $\displaystyle \frac{dy}{dx} = -\frac{y^2}{x^2}$.


    You also know that when $\displaystyle x = 4, y = \frac{4}{7}$.


    So $\displaystyle \frac{dy}{dx}|_{x = 4} = -\frac{\left(\frac{4}{7}\right)^2}{4^2}$

    $\displaystyle = -\frac{\frac{16}{49}}{16}$

    $\displaystyle = -\frac{1}{49}$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    Posts
    98
    thanks but one question.. in step 3 how did you get the -x^2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by tbenne3 View Post
    thanks but one question.. in step 3 how did you get the -x^2?
    What's the derivative of $\displaystyle x^{-1}$?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Implicit Differentiation Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 12th 2010, 10:46 AM
  2. implicit differentiation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 19th 2009, 03:57 PM
  3. Implicit differentiation problem?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 21st 2008, 04:50 PM
  4. Implicit Differentiation Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 9th 2007, 12:50 PM
  5. Implicit Differentiation Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Feb 24th 2006, 11:16 AM

Search Tags


/mathhelpforum @mathhelpforum