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Math Help - Product rule

  1. #1
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    Product rule

    I know there are a thousand ways that people try to explain this. In Calculus for dummies it says (This * that + That * this). But this particular software package that I have called Mathtutor which is outstanding does it a bit differently.

    I understand everything up until the last part.


    Example: Y= ( -2t^2+1) * (3t^2-5)


    Now heres the second to last step to solving the problem:


    Y'= (-12 t^3+ 6t) + (-12 t^3+ 20t)

    Ok folks. I understand that you have to add -12 t^3+ -12 t^3 to get 24 t^3. But what I don't understand is how you do the second part of the equation.

    The answer is Y'= -24 t^3 + 26t

    Sometimes from what my software is explaing the problems to me it adds up the last equation sometimes and other times it will do something like
    Y'= -24 t^3 + 20 t - 6t. What I need to know is what do you descern to properly do the last part of the equation?
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  2. #2
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    Quote Originally Posted by 702 from 512 View Post
    I know there are a thousand ways that people try to explain this. In Calculus for dummies it says (This * that + That * this). But this particular software package that I have called Mathtutor which is outstanding does it a bit differently.

    I understand everything up until the last part.


    Example: Y= ( -2t^2+1) * (3t^2-5)


    Now heres the second to last step to solving the problem:


    Y'= (-12 t^3+ 6t) + (-12 t^3+ 20t)

    Ok folks. I understand that you have to add -12 t^3+ -12 t^3 to get 24 t^3. But what I don't understand is how you do the second part of the equation.

    The answer is Y'= -24 t^3 + 26t

    Sometimes from what my software is explaing the problems to me it adds up the last equation sometimes and other times it will do something like
    Y'= -24 t^3 + 20 t - 6t. What I need to know is what do you descern to properly do the last part of the equation?
    Y^{\prime} = (-12t^3 + 6t) + (-12t^3 + 20t)

    Rearrange this:
    Y^{\prime} = (-12t^3 -12t^3) + (6t + 20t)

    Y^{\prime} = -24t^3 + 26t

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    Y^{\prime} = (-12t^3 + 6t) + (-12t^3 + 20t)

    Rearrange this:
    Y^{\prime} = (-12t^3 -12t^3) + (6t + 20t)

    Y^{\prime} = -24t^3 + 26t

    -Dan
    Ok, what about this?

    Y= (-3x+2) * (-2x-5)

    Second to last step: Which is Y= 6x-4 + 6x + 15 = 12x + 11

    Now why 12x + 11 rather then (-4 + 15) for the last equation?

    Thats what I'm not understanding. Thanks for the quick response. Not trying to make things more complicated then they seem.
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  4. #4
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    I get it.

    I tend to make simple things so complex sometimes. Very simple very easy
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