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Homework Help: Finding the derivative of f?

  1. Jan 10, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of f when

    f(x) = cos(sin(x))

    3. The attempt at a solution

    I used chain rule on this function, and came up with this;

    -sin(sin(x)) times cos(x)

    Now either I'm doing something completely wrong, or I'm not seeing what it is equivalent to in the answers choices online. I would appreciate some hints on how to go about this.
    Last edited: Jan 10, 2013
  2. jcsd
  3. Jan 10, 2013 #2


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    Homework Helper

    Well, you're correct. What are the options given?
  4. Jan 10, 2013 #3
    1. f'(x) = -sin(x) cos(sin(x))

    2. f'(x) = -cos(x) sin(sin(x))

    3. f'(x) = sin(x) cos(cos (x))

    4. f'(x) = -cos(x) sin(cos(x))

    5. f'(x) = cos(x) sin(sin(x))

    6. f'(x) = sin(x) cos(sin(x))

    My feeling is that it's the first one, as it is the only one that has a negative sin, but I could be wrong and I'm not sure how could any of these be the same as my original answer.
  5. Jan 10, 2013 #4

    Ray Vickson

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    Homework Helper

    Why would you say that? You already gave 2) as your answer!
  6. Jan 10, 2013 #5
    Ack! I just realized that it doesn't matter where the negative sign is if there's only multiplication! I feel silly. Thanks for answering for allowing me to see this!
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