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Math Help - Hyperbolic Functions #2

  1. #1
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    Question Hyperbolic Functions #2

     f(x) = arccosh\frac{1}{\sqrt{x^2-7x+x}}
    #1. Find the derivative of the function.
    #2. State the interval where the function is differentiable and calculate the derivative.

    here is my attempted solution so far:
    For  y = cosh^{-1}x, the domain is x \geq 1. So,
     \frac{1}{\sqrt{x^2-7x+x}} \geq 1

     1 \geq \sqrt{x^2-7x+x}

     1 \geq x^2 - 6x - 1

    \frac{6-\sqrt{40}}{2} \leq x \leq \frac{6+\sqrt{40}}{2}

    also \sqrt{x^2-7x+x} \geq 0

    x^2 - 6x \geq 0

    x \geq 0, x \geq 6


    I am also stumped at how to solve the second part of this question. Thanks for any help!
    Last edited by xxlvh; October 26th 2009 at 03:38 PM. Reason: LaTex errors
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  2. #2
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    For starters, you have a serious typo. Is the polynomial under the radical x^2-7x-x, x^2-6x-1, or x^2-6x? You interchange among all three in your question.

    Secondly, rewrite f(x)=a(b(c(x))) where a(x)=\cosh^{-1}(x), b(x)=x^{-1/2}, c(x)=x^2-7x-x, and you can derive using the chain rule: f'(x)=a'(b(c(x)))b'(c(x))c'(x)
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