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Chain rule with leibniz notation

  1. Aug 7, 2010 #1
    1. The problem statement, all variables and given/known data

    If y=f((x2+9)0.5) and f'(5)=-2, find dy/dx when x=4

    2. Relevant equations

    chain rule: dy/dx=(dy/du)(du/dx)

    3. The attempt at a solution

    In my opinion giving f'(5)=-2 is unnecessary as:

    y=f(u)=u, u=(x2+9)0.5

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

    (dy/du)= 1
    (du/dx)= x/((x2+9))0.5

    dy/dx = (1)(x/((x2+9))0.5)
    = x/((x2+9))0.5
    dy/dx(4) = 4/(16+9)0.5
    = 4/(25)0.5
    = 4/5

    the answer is -8/5

    I would appreciate help very much.
  2. jcsd
  3. Aug 7, 2010 #2
    wait, how do you get f(u)=u???
  4. Aug 7, 2010 #3


    Staff: Mentor

    As Annoymage pointed out, you can't assume that f(u) = u.
    y = f(u), so dy/dy = f'(u)
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