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Math Help - Derivative of Inverse Trig Function

  1. #1
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    Derivative of Inverse Trig Function

    Should be relatively simple but not sure what to do after a few attempts...

    q(x)=csc^{ - 1}(x^{ - 1})
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    Quote Originally Posted by drahcirnaw View Post
    Should be relatively simple but not sure what to do after a few attempts...

    q(x)=csc^{ - 1}(x^{ - 1})

    I believe \csc^{ - 1}(x^{ - 1}) = \sin^{-1}(x) ...
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    Ah, makes sense now that the answer is \frac{1}{\sqrt{1-x^2}}.
    Could you show me the steps required to get from the original function to sin^{-1}(x) though? Sorry for the troubles but I'm not seeing it clearly.
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    Quote Originally Posted by drahcirnaw View Post
    Ah, makes sense now that the answer is \frac{1}{\sqrt{1-x^2}}.
    Could you show me the steps required to get from the original function to sin^{-1}(x) though? Sorry for the troubles but I'm not seeing it clearly.
    not much to see, other than knowing that sine and cosecant are reciprocals ...

    if x = \sin{\theta} , then \frac{1}{x} = \csc{\theta}

    inverses ...

    \sin^{-1}(x) = \theta ... \csc^{-1}\left(\frac{1}{x}\right) = \theta
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