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Help required for Directional derivatives

  1. May 6, 2012 #1
    f=9-x^2-y^2 and u=i-j
    The directional derivative comes out to be Du f(x,y)=-sqrt(2)+sqrt(2)

    I'm going to find the directional derivative and could someone kindly point out the mistake because Im getting a different answer and it's important I understand how to do this question:

    Du f(x,y) is simply the ∇f.u (note u is a vector)

    Now ∇f=-2xi-2yj and ∇f.u=(-2xi-2yj).(i-j) = -2x+2y. Help?
     
  2. jcsd
  3. May 6, 2012 #2

    tiny-tim

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    hi hivesaeed4! :smile:

    (try using the X2 button just above the Reply box :wink:)
    no, u must be the unit vector :wink:
     
  4. May 6, 2012 #3
    I hope this does'nt sound stupid but does u always have to be a unit vector. The reason I'm asking is that this is the first time I've heard of it having to be a unit vector.
     
  5. May 6, 2012 #4

    tiny-tim

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  6. May 6, 2012 #5
    So instead of having taken the dot product of u and del of f in the above example I should have taken the dot product of del of f and the unit vector of u.

    Right?
     
  7. May 6, 2012 #6

    tiny-tim

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  8. May 6, 2012 #7
    Thanks alot, tiny-tim.
     
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