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Thread: derivative of trig of a ln of a sqare root questions

  1. October 31st 2012, 10:26 AM #1
    kingsolomonsgrave
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    derivative of trig of a ln of a sqare root questions

    y=tan(ln(sqrt(x^2 +1)))

    find y'

    I got


    sec^2x(ln(sqrt(x^2+1))) * [1/2(x^2+1)] ^ -0.5 /sqrt(x^2+1)

    which is multiplied by the derivative of sqrt (x^2-1) and then multiplied by 2x (the derivative of x^2)

    is there an error in there?
    Last edited by kingsolomonsgrave; October 31st 2012 at 10:30 AM.
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  2. October 31st 2012, 10:51 AM #2
    skeeter
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    Re: derivative of trig of a ln of a sqare root questions

    y = \tan[\ln{\sqrt{x^2+1}}] = \tan \left[\frac{1}{2}\ln(x^2+1)\right]


    \frac{dy}{dx} = \sec^2 \left[\frac{1}{2}\ln(x^2+1) \right] \cdot \frac{x}{x^2+1}
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