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Math Help - bracket expansion and differentiation

  1. #1
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    bracket expansion and differentiation

    need to multiply

    (x^2-1)^4

    I get

    -20x^9+32x^7-12x^5

    Then i need to differentiate this 4 times

    d^4/dx^4 (-20x^9+32x^7-12x^5)

    I get

    -10080x^6+6720x^4-720x^2

    Is this right?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ubhik View Post
    need to multiply

    (x^2-1)^4

    I get

    -20x^9+32x^7-12x^5

    Then i need to differentiate this 4 times

    d^4/dx^4 (-20x^9+32x^7-12x^5)

    I get

    -10080x^6+6720x^4-720x^2

    Is this right?
    Think about this. Your highest power in the expansion will be (x^2)^4 = x^8. So you can't be right.

    By the binomial theorem:
    (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

    You have a = x^2 and b = -1:

    Thus
    (x^2 - 1)^4 = x^8 - 4x^6 + 6x^4 - 4x^2 + 1

    (I'd recommend making sure you know how to do it the long way as well. It's good practice.)

    And make sure you take 4 derivatives. You only took 3.

    -Dan
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  3. #3
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    ok so for the differentiation of
    [(x^2 - 1)^4]

    i got


    1680x^4 - 1440x^2 + 144


    Is this right now?
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  4. #4
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    Hello, ubhik!

    I got: . 1680x^4 - 1440x^2 + 144

    Is this right now? . . . . Yes!
    Good for you!

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  5. #5
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    Quote Originally Posted by ubhik View Post
    ok so for the differentiation of
    [(x^2 - 1)^4]

    i got


    1680x^4 - 1440x^2 + 144


    Is this right now?
    [(x^2 - 1)^4] is an octic, so its derivative is a septic, so whatever anyone else says its derivative cannot be a quartic.

    RonL
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  6. #6
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    Quote Originally Posted by ubhik View Post
    ok so for the differentiation of
    [(x^2 - 1)^4]

    i got


    1680x^4 - 1440x^2 + 144


    Is this right now?
    \frac{d}{dx} (x^2-1)^4 = 4 (x^2-1)^3 (2x)

    RonL
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  7. #7
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    Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ubhik View Post
    Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...
    did the instructions tell you to expand the brackets first? i'd use the chain rule (as CaptainBlack did) 4 times and forget about binomial expansion.
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