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Inverse Function Theorem

  1. Dec 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Use Inverse Function Thm to derive the formula for the derivative of the inverse of sinx on the interval [-pi,2,pi/2]



    2. Relevant equations
    f^-1(f(x))=1/f'(x)



    3. The attempt at a solution
    1/cosx
     
  2. jcsd
  3. Dec 16, 2008 #2

    Mark44

    Staff: Mentor

    I vaguely remember a formula something like the one you show, but I think you have it wrong. f^(-1)(f(x)) on the left side would simplify to just plain x, and I don't see how that would be equal to 1/f'(x).
     
  4. Dec 16, 2008 #3

    Mark44

    Staff: Mentor

    Or maybe not...

    Try this:
    y = sin^(-1)(x) [tex]\iff[/tex] x = sin(y)
    Now differentiate implicitly with respect to x, getting
    1 = cos(y) * dy/dx

    Solve for dy/dx, and in the resulting expression, replace y with what it's equal to.
     
  5. Dec 16, 2008 #4
    Never mind I figured it out.
     
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