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    Hey,

    How would I show that the differentiation of:-

    1 - (2)/(3x^2+2) with a domain of (0,infinite) is always positive? When I differentiate it I get - (12x)/(3X^2+2)^2. Or have I differentiated it wrong? Any help please? Thank you.
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    I can't see what you've written. Too many brackets. Also the use of - doesn't help especially in the first instance. I can hazard a guess though.
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    (Original post by StephenP91)
    I can't see what you've written. Too many brackets. Also the use of - doesn't help especially in the first instance. I can hazard a guess though.
    Sorry, the - is minus sign. I can't use latex .
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    (Original post by FutureMedic)
    Sorry, the - is minus sign. I can't use latex .
    That's not my problem. The first line. 1-(2). Are you saying 1-2 or is it question 1? and then it says -(2) ?

    If it is minus 2, you end up with:

    \dfrac{12x}{(3x^{2} + 2)^{2}}

    Then you can just simply say 12x is always a positive value for x belonging to the positive real numbers and since the domain is only the positive reals then this is fine. (3x^{2} + 2)^{2} is postive regardless of whether or not x is negative or positive. Then just conclude saying that a positive value divided by a positive value is always positive.
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    Differentiate again to find d2y/dx2
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    (Original post by StephenP91)
    That's not my problem. The first line. 1-(2). Are you saying 1-2 or is it question 1? and then it says -(2) ?

    If it is minus 2, you end up with:

    \dfrac{12x}{(3x^{2} + 2)^{2}}

    Then you can just simply say 12x is always a postively value for x belonging to the positive real numbers. (3x^{2} + 2)^{2} is postive regardless of whether or not x is negative or positive. Then just conclude saying that a positive value divided by a positive value is always positive.
    Hi,

    It's 1 minus the fraction numerator (2), denominator (3x^2+2).
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    (Original post by FutureMedic)
    Hi,

    It's 1 minus the fraction numerator (2), denominator (3x^2+2)^2.
    Alrighty then. Just read what I said in the previous post.
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    (Original post by StephenP91)
    Alrighty then. Just read what I said in the previous post.
    Thank you.
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    (Original post by StephenP91)
    Alrighty then. Just read what I said in the previous post.
    Isn't there a minus when it's differentiated though coming from the ^-1?
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    (Original post by FutureMedic)
    Isn't there a minus when it's differentiated though coming from the ^-1?
    \dfrac{-2}{3x^{2}+2}

    The minus 1 you bring up is made plus by your -2.

    (3x^{2}+2)^{-1}

    Differentiate that.

    -6x(3x^{2}+2)^{-2}

    Then when you multiply that by the -2, you get what I previously said.
 
 
 
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