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The Derivative of CSC^2 u

  1. Mar 29, 2008 #1
    1. The problem statement, all variables and given/known data

    the derivative of CSC u is CSC u times cot u times the derivative of the u
    but how can I derive CSC^2 u?


    2. The attempt at a solution


    CSC^2 u is (CSC u)^2

    The derivative is
    2(CSC u)(CSC u times Cot u)(1)

    another way

    CSC^2 u = CSC u times CSC u
    CSC u times ( CSC u Cot u )(1) + CSC u ( CSC u Cot u)(1)

    Is it correct?
     
  2. jcsd
  3. Mar 29, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi racer! :smile:

    Yes they're both right!

    (d/du)cosec^2(u) = 2cosec^2(u)cot(u).

    You used both substitution and the product rule … they both work in this case, and either is fine. :smile:

    (Though personally, I'd always go for substitution.)
     
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