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Math Help - Please help me derive this!!

  1. #1
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    Please help me derive this!!

    f(x)= e^(-1/(sin^2(x)) , -pi/2<x<pi/2 , x=/=0
    f(x)= 0 , x=0

    Can someone explain to me what these ranges mean? Do they have any effect on the derivitive? THANKS!
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by shmayer View Post
    f(x)= e^(-1/(sin^2(x)) , -pi/2<x<pi/2 , x=/=0
    f(x)= 0 , x=0

    Can someone explain to me what these ranges mean? Do they have any effect on the derivitive? THANKS!

    f'(x)= e^{\frac{-1}{sin^2x}} (\frac{-1}{sin^2x})'

    Find this separately:
    (-sin^{-2}x)' =  2 sin^{-3}x cos x

    Then combine. Good luck!
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  3. #3
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    THANKS!
    ....if you can answer this, how would i find the second derivative? It would be the same as the first derivative just multiplied by the derivative of 2sin^-3(x)cosx..but how would i derive this ?? Thanks again
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