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Math Help - Differentiation Problem

  1. #1
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    Differentiation Problem

    Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

    differentiate 5x(9-3x)

    so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

    Help much appreciated.

    Many thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by EternalChicken View Post
    Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

    differentiate 5x(9-3x)

    so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

    Help much appreciated.

    Many thanks
    In this case just expand the brackets and the differentiate the quadratic
    that results:

    d/dx [5x(9-3x)] = d/dx [45x - 15 x^2] = 45 -30x

    RonL
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  3. #3
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    Ah, of course. Seems so obvious now :P

    Many thanks for your speedy reply.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by EternalChicken View Post
    Hey. Have a question for my work, and need a little help getting the answer. Have been looking up the chain rule for some previous questions, but am now stuck, as i have not had one like this before. I'm not gonna give the actual question, as i want to work that out myself, but here is how it is styled:

    differentiate 5x(9-3x)

    so, normally that would be ok, but i havent had one with an x n the outside of the brackets, and am not sure what to do with it. Do i turn it into 5? but then that wouldn't make sense with the chain rule, so do i leave 5x as it is...

    Help much appreciated.

    Many thanks
    Or you can think of this as a product:
    d/dx[(5x)(9 - 3x)] = d/dx[5x]*(9 - 3x) + (5x)*d/dx[3 - 9x] = (5)*(9 - 3x) + (5x)*(-3)

    = 45 - 15x - 15x = 45 - 30x

    -Dan
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