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Math Help - hyperbolic derivatives

  1. #1
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    hyperbolic derivatives

    y = tanh^-1 x + ln sqrt(1-x^2)

    then i know tanh^-1 = 1/2ln (1+x)/(1-x) + ln sqrt(1-x^2) but lost pretty much there after.

    then a none hyperbolic derivative

    y = x cos ^1 x - sqrt(1-x^2)

    do I use the chain rule in both of these cases? or if not what rule would I use ?
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  2. #2
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    Quote Originally Posted by UMStudent View Post
    y = tanh^-1 x + ln sqrt(1-x^2)

    then i know tanh^-1 = 1/2ln (1+x)/(1-x) + ln sqrt(1-x^2) but lost pretty much there after.

    then a none hyperbolic derivative

    y = x cos ^1 x - sqrt(1-x^2)

    do I use the chain rule in both of these cases? or if not what rule would I use ?
    The language in this question is confusing!

    I presume you need to find the derivative of:
    y = tanh^-1 x + ln sqrt(1-x^2)

    Since d/dx[tanh^-1 x] = -1/[(x - 1)(x + 1)]
    Then
    dy/dx = -1/[(x - 1)(x + 1)] + 1/sqrt(1 - x^2) * (1/2)*1/sqrt(1 - x^2) * (-2x)
    via the chain rule. (I'll let you simplify this.)

    And I presume you need to find the derivative of:
    y = x cosh^-1 x - sqrt(1-x^2)

    Since d/dx[cosh^-1 x] = 1/sqrt[(x - 1)(x + 1)]
    Then
    dy/dx = 1 * cosh^-1x + x * 1/sqrt[(x - 1)(x + 1)] + (1/2) * 1/sqrt(1 - x^2) * (-2x)
    via the product and chain rules. (Again, you need to simplify this.)

    -Dan
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  3. #3
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    Thanks for the help appreciate it. Sorry for the vauge-ness.
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