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Simplifying this derivative...

  1. Jun 27, 2017 #1
    1. The problem statement, all variables and given/known data
    Evaluate the derivative of the following function:
    f(w)= cos(sin^(-1)2w)
    2. Relevant equations
    Chain Rule

    3. The attempt at a solution
    I did just as the chain rule says where
    F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2))

    but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))

    and I'm wondering if there is some kind of simplification I'm missing. Why would sin and sin^(-1) disappear?
  2. jcsd
  3. Jun 27, 2017 #2


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    Science Advisor
    Homework Helper

    Because they are inverse functions. ##\sin(\sin^{-1}(x))=x##.
  4. Jun 27, 2017 #3
    Ah okay. I wasn't aware of this. Thank you.
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