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Math Help - differentiate and simplify #5

  1. #1
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    differentiate and simplify #5

    Can someone please check my answers below for accurateness? The instructions are: Differentiate and simplify.

    1) y=(2x^2+3x-1)(3x^2-5x-3)
    y'=(4x+3)(3x^2-5x-3)+(2x^2+3x-1)(6x-5)

    2) y=(5x^2+3x-1)(3x^2-5x-3)
    y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)

    3)y=6x^3-7x^2+5x-7+x^(5/3)-7/(x^3)
    y'=18x^2-14x+5+5x^(2/3)+21/(x^4)

    4) y=[5x^4-3x^3+6x^2-5x+7-x^(3/2)]/x^2
    y'=10x-3+5/(x^2)-14/(x^3)+1/(2((sqrt)x)^3)

    5) y=(5x^2-3x+7)(3x^2+7x-2)(6x^2+4x-5)
    y'=(10x-3)(3x^2+7x-2)(6x^2+4x-5)+(5x^2-3x+7)(6x+7)(6x^2+4x-5)+(5x^2-3x+7)(3x^2+7x-2)(12x+4)

    6) y=(7x^3-5x^2+6x-3)^12
    y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11

    7) y=(4x^2+3)^5(2x^2-1)^4
    y'=[8x(4x^2+3)^4(2x^2-1)^3][5(2x^2-1)+2(4x^2+3)]

    8) y=(4x^2+3x-5)^(4/5)
    y'=[4(8x+3)]/[5(4x^2+3x-5)^(1/5)]

    O.K. Bold the wrong answers or let me know which ones I should double check and fix. Thanks for your help and I really appreciate it because there are no answers to these questions in the back of the book, so I need to know if they are correct. Thank you once again!
    Last edited by mr fantastic; August 12th 2009 at 05:03 PM. Reason: Changed post title
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  2. #2
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  3. #3
    Super Member Failure's Avatar
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    Quote Originally Posted by skeske1234 View Post
    Can someone please check my answers below for accurateness? The instructions are: Differentiate and simplify.

    1) y=(2x^2+3x-1)(3x^2-5x-3)
    y'=(4x+3)(3x^2-5x-3)+(2x^2+3x-1)(6x-5)
    Differentiation was ok - but you should now simplify.

    2) y=(5x^2+3x-1)(3x^2-5x-3)
    y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)
    Differentiation is not ok. Where on earth did you get that factor 4x^2-3? The second factor was (3x^2-5x-3), no?
    And, again, you need to simplify.

    3)y=6x^3-7x^2+5x-7+{\color{red}x^(5/3)}-7/(x^3)
    y'=18x^2-14x+5+5x^(2/3)+21/(x^4)
    Almost, but not quite: everything seems ok except the term 5x^{5/3}. Think about it. Did you apply the power rule correctly? I don't think so.

    4) y=[5x^4-3x^3+6x^2-5x+7-x^(3/2)]/x^2
    y'=10x-3+5/(x^2)-14/(x^3)+1/(2((sqrt)x)^3)
    Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.

    5) y=(5x^2-3x+7)(3x^2+7x-2)(6x^2+4x-5)
    y'=(10x-3)(3x^2+7x-2)(6x^2+4x-5)+(5x^2-3x+7)(6x+7)(6x^2+4x-5)+(5x^2-3x+7)(3x^2+7x-2)(12x+4)
    Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. y is a polynomial of degree 6, therefore y' must be a polynomial of degree 6-1=5. I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...

    6) y=(7x^3-5x^2+6x-3)^12
    y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11
    Differentiation seems ok to me. (I'm a little surprised to see you put the "inner derivative" 21x^2-10x+6 as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out

    7) y=(4x^2+3)^5(2x^2-1)^4
    y'=[8x(4x^2+3)^4(2x^2-1)^3][5(2x^2-1)+2(4x^2+3)]
    No, for some reason you have botched this one up completely. What about
    y'=5(4x^2+3)^4\cdot 8x\cdot (2x^2-1)^4+(4x^2+3)^5\cdot 4(2x^2-1)^3\cdot 4x
    Now here, you would simplify by factoring out (4x^2+3)^4\cdot (2x^2-1)^3

    8) y=(4x^2+3x-5)^(4/5)
    y'=
    Judging from the above, you should be able to differentiate this one as well.
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  4. #4
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    Quote Originally Posted by Failure View Post
    Differentiation was ok - but you should now simplify.



    Differentiation is not ok. Where on earth did you get that factor 4x^2-3? The second factor was (3x^2-5x-3), no?
    And, again, you need to simplify.


    Almost, but not quite: everything seems ok except the term 5x^{5/3}. Think about it. Did you apply the power rule correctly? I don't think so.


    Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.


    Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. y is a polynomial of degree 6, therefore y' must be a polynomial of degree 6-1=5. I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...


    Differentiation seems ok to me. (I'm a little surprised to see you put the "inner derivative" 21x^2-10x+6 as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out


    No, for some reason you have botched this one up completely. What about
    y'=5(4x^2+3)^4\cdot 8x\cdot (2x^2-1)^4+(4x^2+3)^5\cdot 4(2x^2-1)^3\cdot 4x
    Now here, you would simplify by factoring out (4x^2+3)^4\cdot (2x^2-1)^3


    Judging from the above, you should be able to differentiate this one as well.
    #1.. how do I simplify this? isn't it already in lowest terms
    #2.. I used the the product rule to get that answer
    3.. sorry in red supposed to be 5/3 x^(2/3) now correct?
    8.. my answer is y'=[4(8x+3)]/[5(4x^2+3x-5)^1/5)] is this correct?
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  5. #5
    Super Member Failure's Avatar
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    Quote Originally Posted by skeske1234 View Post
    #1.. how do I simplify this? isn't it already in lowest terms
    Well, maybe your teacher has a different idea of what "simplifying" means. But if you multiply y' out and collect same powers of x you get y'=24x^3 - 3x^2 - 48x - 4. Looks simpler to me...

    #2.. I used the the product rule to get that answer
    No, you didn't. Because if you did, the second factor of the first term would look differently: as I wrote.

    3.. sorry in red supposed to be 5/3 x^(2/3) now correct?
    Yes.

    8.. my answer is y'=[4(8x+3)]/[5(4x^2+3x-5)^1/5)] is this correct?
    Yes.
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