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Directional derivative?

  1. Jan 12, 2007 #1
    Im doing the following question:

    calculate the directional derivative of the function f(x,y,z) = z/(2x + y) at the point (0,1,1) in the direction d = 2i - 2j - k

    could someone please check my answer is correct as i calculated -3i -6k

    Also how do i find the unit vector in the direction of the greatest rate of change of the function f(x,y,z)

    thanks
     
  2. jcsd
  3. Jan 12, 2007 #2

    Dick

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    Think again. The directional derivative of a scalar function is not a vector. Hint: look at the concept of gradient.
     
  4. Jan 12, 2007 #3
    the gradient i found was -2z/(2x+y)^2 i + -z/(2x+y)^2 j + 2x+y/(2x+y)^2 k

    i thought the directional derivative was then s.grad

    what should the answer be?
     
  5. Jan 12, 2007 #4

    Dick

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    It IS s.grad. But s.grad is a scalar.
     
  6. Jan 12, 2007 #5
    ok sorry. i think iv got the answer now. -1 ????
     
  7. Jan 12, 2007 #6

    Dick

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    What is your vector for grad? You'd better check arithmetic...
     
  8. Jan 12, 2007 #7

    Dick

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    I've gotta go now. But as for your second question, if derivative is s.grad, what direction should s point to maximize the derivative?
     
  9. Jan 12, 2007 #8
    how about -3?
     
  10. Jan 13, 2007 #9

    Dick

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    -3? I like it.
     
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