Results 1 to 5 of 5

Math Help - Implicit diff. problem

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    36

    Implicit diff. problem

    I'm having trouble with this problem:

    Solve using implicit differentiation

    x\sqrt{y+1}=xy+1

    x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}\cdot(1)=xy+1

    x\cdot\frac{1}{2}\cdot\frac{1}{\sqrt{y+1}}=xy+1

    \frac{x}{2\sqrt{y+1}}=xy+1

    Am I heading in the right direction? Where do I go from here?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by ascendancy523 View Post
    I'm having trouble with this problem:

    Solve using implicit differentiation

    x\sqrt{y+1}=xy+1

    x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}\cdot(1)=xy+1

    x\cdot\frac{1}{2}\cdot\frac{1}{\sqrt{y+1}}=xy+1

    \frac{x}{2\sqrt{y+1}}=xy+1

    Am I heading in the right direction? Where do I go from here?
    Well, not really the right direction.

    Starting with

    x\sqrt{y+1}=xy+1

    Differentiate both sides with respect to x:

    \displaystyle x\cdot\frac{1}{2}(y+1)^{-\frac{1}{2}}\cdot\frac{dy}{dx}+\sqrt{y+1}=x\cdot \frac{dy}{dx}+y

    Solve for \displaystyle\frac{dy}{dx} in terms of \displaystyle x and \displaystyle y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    36
    Quote Originally Posted by undefined View Post
    Well, not really the right direction.

    Starting with

    x\sqrt{y+1}=xy+1

    Differentiate both sides with respect to x:

    \displaystyle x\cdot\frac{1}{2}(y+1)^{-\frac{1}{2}}\cdot\frac{dy}{dx}+\sqrt{y+1}=x\cdot \frac{dy}{dx}+y

    Solve for \displaystyle\frac{dy}{dx} in terms of \displaystyle x and \displaystyle y.
    So maybe:

    x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}\cdot\frac{dy}{dx}-x\frac{dy}{dx}=-\sqrt{y+1}+y

    \frac{dy}{dx}[x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}-x]=-\sqrt{y+1}+y

    \frac{dy}{dx}=\frac{-\sqrt{y+1}+y}{x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}-x}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by ascendancy523 View Post
    So maybe:

    x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}\cdot\frac{dy}{dx}-x\frac{dy}{dx}=-\sqrt{y+1}+y

    \frac{dy}{dx}[x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}-x]=-\sqrt{y+1}+y

    \frac{dy}{dx}=\frac{-\sqrt{y+1}+y}{x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}-x}
    Looks good.

    Edit: One small note: make sure this is what the problem statement asks for. You just said "solve using implicit differentiation" and I gave this answer because that is what is typically asked for.
    Last edited by undefined; June 22nd 2010 at 11:08 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2010
    Posts
    36
    Yes, this is exactly what the problem has asked for. Thank you!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. implicit diff. with logs
    Posted in the Calculus Forum
    Replies: 10
    Last Post: December 6th 2009, 03:44 PM
  2. Help with Implicit Diff.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 7th 2008, 07:08 AM
  3. implicit diff
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 30th 2008, 09:50 AM
  4. implicit diff.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 9th 2007, 06:26 PM
  5. diff implicit functn
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 5th 2006, 11:12 AM

Search Tags


/mathhelpforum @mathhelpforum