Results 1 to 3 of 3

Math Help - Implicit differentiation

  1. #1
    Senior Member
    Joined
    Sep 2013
    From
    Portland
    Posts
    448
    Thanks
    64

    Implicit differentiation

    I just started implicit differentiation but something just confused me, maybe perhaps because I have had an incredibly long day and I am tired.

    The question is to find the equation of a tangent line, I am fine with the part. the curve is y^5 + x^2y -2x^2 = -1 and the point is (sqrt2, 1)

    okay, so I know to differentiate both sides. what I need help with is it differentiates to

    5y^4[dy/dx] + 2xy + x^2[dy/dx] - 4x = 0

    now I know the final result is dy/dx = [2sqrt2]/7

    the part confusing me is in the earlier examples [dy/dx] would be placed next to the y variable like x/2 + 2y[dy/dx] = 0 which yields dy/dx = - x/4y.

    Can someone explain the placement of [dy/dx] in my example above. I feel like I probably know the answer but like I said it was an incredibly long day. Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    828
    Thanks
    209

    Re: Implicit differentiation

    Implicit differentiation-06-oct-13.png
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Sep 2013
    From
    Portland
    Posts
    448
    Thanks
    64

    Re: Implicit differentiation

    at first I didn't realize what you meant by w r t x, haha

    okay I understand.

    y^5 is differentiate y wrtx and using the product rule for x^2y, y is being differentiated in x^2[d/dx]y but not in d/dx[x^2] * y
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 11
    Last Post: April 3rd 2010, 06:24 AM
  3. Implicit Differentiation #3
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 8th 2009, 12:14 PM
  4. More Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 30th 2007, 06:38 PM
  5. Even More Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 29th 2007, 10:53 PM

Search Tags


/mathhelpforum @mathhelpforum