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Math Help - Help with a question involving chain rule + product rule (derivative)

  1. #1
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    Help with a question involving chain rule + product rule (derivative)

    I'm having trouble finding the derivative of this function: x(3x - 9)^3

    The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

    Thanks in advance.
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    Quote Originally Posted by Archduke01 View Post
    I'm having trouble finding the derivative of this function: x(3x - 9)^3

    The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

    Thanks in advance.
    Set f(x) = x and g(x) = (3x - 9)^3. First calculate f'(x) and g'(x) individually using the chain rule. Then use the product rule to get d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x), substituting in the values you found for all of these functions.
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  3. #3
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    Quote Originally Posted by Archduke01 View Post
    I'm having trouble finding the derivative of this function: x(3x - 9)^3

    The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

    Thanks in advance.

    (x(3x-9)^3)' =1*(3x-9)^3+x*9(3x-9)^2=(3x-9)^2(3x-9+9x)=
    9(x-3)^2(12x-9)=27(x-3)^2(4x-3)

    Tonio
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    Thanks so much for clarifying, guys. I appreciate it.
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  5. #5
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    Quote Originally Posted by tonio View Post
    (x(3x-9)^3)' =1*(3x-9)^3+x*9(3x-9)^2=(3x-9)^2(3x-9+9x)=
    9(x-3)^2(12x-9)=27(x-3)^2(4x-3)

    Tonio
    I don't understand that second line. Why is it 1*(3x-9)^3+x*9(3x-9)^2?
    Last edited by Archduke01; October 19th 2009 at 01:50 PM.
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    Quote Originally Posted by Archduke01 View Post
    I don't understand that second line. Why is it 1*(3x-9)^3+x*9(3x-9)^2?

    Derivative of the first times the second plus the first times the derivative of the 2nd...the formula for derivative of a product! Of course, the second factor is composed, so you've to apply the chain rule ot it.

    Tonio
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