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Hello Chain rule!

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data

    h(x) = f[g(x)]

    h'(x) = f'[g(x)] * g'(x)

    2. Relevant equations

    h(x) = sin(-x)

    3. The attempt at a solution

    So, this one is pretty simple, except I just want to confirm something. When I do it it, it looks like this:

    The derivative of sin = cos,

    so you have

    h(x) = cos(-x)

    then you multiply the outside by g'(x). The derivative of -x is negative one. So it's

    h(x) = cos(-x) * -1

    h(x) = -cos(-x)

    h'(x) = cos(x)

    But the computer program bagatrix insists the final answer is

    h'(x) = -cos(x)

    Am I wrong, and if so, where did I go wrong?
     
  2. jcsd
  3. May 7, 2013 #2
    Cosine is an even function.
     
  4. May 7, 2013 #3
    As in the opposite angle identity?

    sin(-x) = -sin(x)

    and

    cos(-x) = cos(x) ?
     
  5. May 7, 2013 #4

    MarneMath

    User Avatar
    Education Advisor

    Never heard it called that, but yes to the above. A good way to have checked this is to look at the unit circle :]
     
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