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Review in Variable Differentiation

  1. Jan 11, 2013 #1
    Please see attached.

    I was looking for an explanation of the answer I have attached. Its been a little while and was just looking for the logic behind the differentiation shown for this problem. Its basically an optimization problem where I am looking for the minimum angle (theta) for the least amount of force for T_ab.

    Thanks
     

    Attached Files:

  2. jcsd
  3. Jan 11, 2013 #2

    haruspex

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    It uses the standard rule for differentiating a quotient: d(u/v) = (vdu - udv)/v2
     
  4. Jan 12, 2013 #3

    HallsofIvy

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    You can also do the differentiation of a quotient as the differentiation of a product using the chain rule: [itex]u/v= uv^{-1}[/itex] so that
    [tex](u/v)'= (uv^{-1})'= u'v^{-1}+ u(v^{-1})'= u'v^{-1}+ u(-v^{-2}v')[/tex]
    [tex]= \frac{u'}{v}+ \frac{uv'}{v^2}= \frac{u'v}{v^2}+ \frac{uv'}{v^2}= \frac{u'v+ uv'}{v^2}[/tex]
     
  5. Jan 12, 2013 #4

    haruspex

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    [tex]= \frac{u'}{v}- \frac{uv'}{v^2}[/tex] etc.
     
  6. Jan 17, 2013 #5
    Thanks for the response.

    So differentiating D-LCos(theta) the constant D goes to 0 and the -LCos(theta) goes to +Lsin(theta) ...then multiply that by sin(theta) in the denominator to get Lsin^2(theta).....

    However I was curious why nothing happens to the L....in front of the Cos.

    Thanks
     
  7. Jan 18, 2013 #6

    HallsofIvy

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    "L" is a constant. What do you think should happen to it?
     
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