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Math Help - PLease Help Me!

  1. #1
    Senior Member
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    PLease Help Me!

    My brain Gave up on this problem....
    Find the derivative:
    D_x(3x^3 + x^{-3})(x+3)(x^2-5)
    Thanks ahead
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    My brain Gave up on this problem....
    Find the derivative:
    D_x(3x^3 + x^{-3})(x+3)(x^2-5)
    Thanks ahead
    Use the product rule:

    D_x(3x^3 + x^{-3})(x+3)(x^2-5)= <br />
D_x[3x^3+x^{-3}]\ (x+3) (x^2-5) + (3x^3+x^{-3}) D_x[(x+3)(x^2-5)]

    ...... =(9x^2-3x^{-4})(x+3)(x^2-5) +(3x^3+x^{-3}) [(x^2-5)+(x+3)(2x)]

    I will leave simplifying this further to you.

    RonL
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  3. #3
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    My answer is:
    18x^5+45x^4-60x^3-120x^2-3x^{-2}-5x^{-3}
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  4. #4
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    Hello, ^_^Engineer_Adam^_^!

    Find the derivative: . y \:=\:(3x^3 + x^{-3})(x+3)(x^2-5)

    There is an extended product rule . . .

    If y \:=\:f\!gh, then: . y' \;=\;f'gh + f\!g'h + f\!gh'

    If y \:=\:f\!ghk, then: . y' \;=\;f'ghk + f\!g'hk + f\!gh'k + f\!ghk'

    . . Get the pattern?

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    If you're going to mutlply-out your final answer,
    . . you might as well multiply first . . .

    We have: . y \;=\;3x^6 + 9x^5 - 15x^4 - 45x^3 + 1 - 3x^{-1} - 5x^{-2} - 15x^{-3}

    Then: . y' \;=\;18x^5 + 45x^4 - 60x^3 - 135x^2 + 3x^{-2} + 10x^{-3} + 45x^{-4}

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