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Math Help - Help with Derivative problem involving ARCSIN

  1. #1
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    Help with Derivative problem involving ARCSIN

    Directions: Find the derivative of y with respect to the appropriate variabl.

    y=sin^-1(2t)^1/2

    Sin^-1 is the ARCSIN, and is the part I'm having trouble with. The answer is Square root of 2 over the square root of (1 - 2t^2), but I need help on how to obtain that answer. Thanks for your help!
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  2. #2
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    Quote Originally Posted by Alex225 View Post
    Directions: Find the derivative of y with respect to the appropriate variabl.

    y=sin^-1(2t)^1/2

    Sin^-1 is the ARCSIN, and is the part I'm having trouble with. The answer is Square root of 2 over the square root of (1 - 2t^2), but I need help on how to obtain that answer. Thanks for your help!
    The derivative of y = \sin^{-1} (2t)^{1/2} (what you posted) is NOT \frac{\sqrt{2}}{\sqrt{1 - 2t^2}}.

    For the given answer to be correct the question should be find the derivative of y = \sin^{-1} (2^{1/2} t).

    In which case you let u = 2^{1/2} t and use the chain rule. You should know that if y = \sin^{-1} u then \frac{dy}{du} = \frac{1}{\sqrt{1 - u^2}} ....
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