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Math Help - differentiate question

  1. #1
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    differentiate question

    How can u differentiate that :

    c= 100,000* (x^2 + 25 )^0.5 + 75,000(8-x)

    thnx
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  2. #2
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    dc/dx=100,000*0.5*(x^2+25)^(-0.5).2.x+75,000(-1)
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  3. #3
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    Quote Originally Posted by Pulock2009 View Post
    dc/dx=100,000*0.5*(x^2+25)^(-0.5).2.x+75,000(-1)

    thnx , that is what I got

    but I'm confused how to get the critical value of x

    how can that equation be simplified in order to get the value of x

    thnx again
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  4. #4
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    dc/dx=0 and solve ,friend!!!
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  5. #5
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    Quote Originally Posted by Pulock2009 View Post
    dc/dx=0 and solve ,friend!!!
    the first part is raised to the power 0.5 which is kind of problem for me

    any suggestion ?
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  6. #6
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    A power of 0.5 is the same as taking a square root. So: a^{0.5} = a^{1/2} = \sqrt{a}

    If it is negative: a^{-0.5} = a^{-1/2} = \frac{1}{a^{1/2}} = \frac{1}{\sqrt{a}}

    Does that help?
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  7. #7
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    Quote Originally Posted by zisi View Post
    the first part is raised to the power 0.5 which is kind of problem for me

    any suggestion ?
    Surely you know that the derivative of x^n is nx^{n-1}. That's true for n any number. Even 0.5.

    The derivative of x^{0.5} is 0.5x^{-0.5} which, as drumist points out, could also be written \frac{0.5}{\sqrt{x}}.

    However, if the original problem was given as x^{0.5} then I would recommend writing the answer in the same way: 0.5x^{-0.5}.
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