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Math Help - [SOLVED] derivatives

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    [SOLVED] derivatives

    The derivative of (1 + (x^2 + 1)^1/2)^1/2

    I'm not really sure how to start this problem out... I see that the chain rule applies.... Would (1 + (x^2 + 1)^1/2) be considered g(x)? Can you show me the steps, please?


    Here are the possible answers:
    A) 1/4(1 + sq rt(x^2 + 1))^-1/2(x^2 + 1)^-1/2

    B) 1/2(1 + sq rt(x^2 + 1))^-1/2(x/sq rt(x^2 + 1))

    C) 1/2(1 + sq rt(x^2 + 1))

    D) 1/2(1 + sq rt(x^2 + 1))^-1/2(2x)
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    Quote Originally Posted by obsmith08 View Post
    The derivative of (1 + (x^2 + 1)^1/2)^1/2

    I'm not really sure how to start this problem out... I see that the chain rule applies.... Would (1 + (x^2 + 1)^1/2) be considered g(x)? Can you show me the steps, please?
    You will need to use the chain rule more than once:

    \frac d{dx}\left[1 + (x^2 + 1)^{1/2}\right]^{1/2}

    =\frac12\left[1 + (x^2 + 1)^{1/2}\right]^{-1/2}\cdot\frac d{dx}\left[1 + (x^2 + 1)^{1/2}\right]

    =\frac12\left[1 + (x^2 + 1)^{1/2}\right]^{-1/2}\cdot\frac12\left(x^2 + 1\right)^{-1/2}\cdot\frac d{dx}\left[x^2+1\right]

    =\frac12\left[1 + (x^2 + 1)^{1/2}\right]^{-1/2}\cdot\frac12\left(x^2 + 1\right)^{-1/2}\cdot2x

    Now you can clean it up.
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