Results 1 to 6 of 6

Math Help - Chain rule using Leibniz notation.

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    171

    Chain rule using Leibniz notation.

    Using Leibniz notation, apply the chain rule to determine dy/dx at x=4.

    y=u^2+3u, u=square root of x

    So I rewrite square root of x as x^1/2

    dy/du = 1/2x^-1/2

    du/dx = 2u+3

    dy/dx = (dy/du)(du/dx)

    = 1/2x^-1/2 (2u+3)

    = 1/2x^-1/2 [2(x^1/2)+3] *subbed in u

    = 2(x^1/2)+3 / 1/2x^1/2

    = 2(x^1/2)+3 / square root of 1/2x

    The answer is 7/4, however my answer when I sub in x=4 is 7/1.414213562

    What did I do wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member eddie2042's Avatar
    Joined
    Apr 2010
    Posts
    70
    Thanks
    1
    y=u^2+3u, u=square root of x
    um.. if you sub in sqrt(x) to the u^2 wouldn't that make it

    y = x + 3sqrt(x)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    171
    = 1/2x^-1/2 (2u+3)

    = 1/2x^-1/2 [2(x^1/2)+3]

    I subbed in u, which is u=x^1/2, in the u in the 2u+3 part. Wouldn't that make it 2(x^1/2)+3?

    Oh I see what you did. Are you supposed to sub in u right away?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    \frac{dy}{du} = 2u+3
    \frac{du}{dx} = \frac{1}{2\sqrt{x}}

    \frac{dy}{du}\frac{du}{dx} = \frac{2u+3}{2\sqrt{x}} = \frac{2\sqrt{x}+3}{2\sqrt{x}} and x=4...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    171
    reworking
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2009
    Posts
    171
    solved it,.. thanks
    Last edited by kmjt; April 2nd 2010 at 03:33 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. leibniz notation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 23rd 2011, 08:51 AM
  2. Replies: 1
    Last Post: March 10th 2011, 03:23 AM
  3. Leibniz formula and chain rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 26th 2010, 03:07 PM
  4. Leibniz notation.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 9th 2010, 05:20 AM
  5. Chain Rule Leibniz Notation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 7th 2010, 06:55 PM

Search Tags


/mathhelpforum @mathhelpforum