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Derivative of function

  1. Jan 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Compute the derivative of the following function.

    2. Relevant equations

    f:[1,-1] arrow [-pie/2, pie/2] given by f(x)=sin^-1 (x)

    3. The attempt at a solution

    I know that f ' (x)=1/[sqrt(1-x^2)]

    Im not sure how to include the intervals of pie given, not sure what they want me to do.
  2. jcsd
  3. Jan 16, 2009 #2


    Staff: Mentor

    Knowing what the derivative is doesn't do you much good if you have compute it.

    Do you know about implicit differentiation?

    If so, letting y = f(x), you have y = sin-1(x)
    Solve this equation for x, and then calculate dy/dx.

    When you do this, you should get dy/dx = 1/cos(sin-1(x)), which you can simplify further. That's where the interval [-pi, pi] comes into play.

    BTW, the name of the Greek letter [itex]\pi[/itex] is pi, not pie.
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