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Thread: derivative

  1. #1
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    derivative

    wonder if anyone know what the derivate to y = ln(x + sqrt(1+x^2)) is ??

    :/
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  2. #2
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    y = 1/sqrt(x^2+1)

    right ?
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  3. #3
    MHF Contributor Amer's Avatar
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    no it is not rite
    \displaystyle ln\left( x + \sqrt{1+x^2}\right)

    in general if

    y=\displaystyle ln\left(f(x) \right)

    y' = \frac{f'(x)}{f(x)}

    so...
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  4. #4
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    (1/sqrt(x^2+1)) / (ln(x + sqrt(1+x^2))) ?
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  5. #5
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    Quote Originally Posted by paulaa View Post
    (1/sqrt(x^2+1)) / (ln(x + sqrt(1+x^2))) ?
    no again ...

    \dfrac{d}{dx} \left[\ln(x+\sqrt{1+x^2})\right] = \dfrac{1+\frac{x}{\sqrt{1+x^2}}}{x + \sqrt{1+x^2}}
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  6. #6
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    So she was right the first time!

    (Which figures, for the log form of arcsinh.)
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