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Math Help - [SOLVED] DERIVATIVE OF sin^-1 x

  1. #1
    jonny4407
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    [SOLVED] DERIVATIVE OF sin^-1 x

    using chain rule or inverse function rule, how can you prove that sin^-1 x is equal to 1/(sqrt(1-x^2))
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  2. #2
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    Quote Originally Posted by jonny4407
    using chain rule or inverse function rule, how can you prove that sin^-1 x is equal to 1/(sqrt(1-x^2))
    The best way to do it is to use right triangles. Start with this info.

    \sin^{-1}(x)=y

    So, taking the sine of both sides gives us that \sin(y)=x

    Draw a triangle with y as the angle, and make the sine of y equal to x. Differentiate both sides of you equation, and solve for \frac{dy}{dx}.

    Good luck.
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