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Math Help - quick differentiation :)

  1. #1
    Junior Member shepherdm1270's Avatar
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    quick differentiation :)

    hey guys, quick question, how do you use the product rule to differentiate something with more than 2 terms... for example:

    3x^2y^3


    I think I'm finally gettin the hang of this stuff guys thanks for all the help
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by shepherdm1270 View Post
    hey guys, quick question, how do you use the product rule to differentiate something with more than 2 terms... for example:

    3x^2y^3


    I think I'm finally gettin the hang of this stuff guys thanks for all the help
    That is two terms, but say you have the following...

    \sin(x)e^x x^2

    This is a product of three terms. You always split products into two terms like so:

    \sin(x) * e^x x^2

    The derivative follows the product rule TWICE over...

    \cos(x) e^x x^2 + (e^x x^2)' \sin(x)

    \cos(x) e^x x^2 + \sin(x)(e^x x^2 + 2x e^x)
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  3. #3
    Junior Member shepherdm1270's Avatar
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    hmmm... ok so using implicit differentiation for this problem i got this so far:

    x^4 + 3 x^2 y^3 - y^2 = 5

    d/dx ( x^4 + 3 x^2 y^3 - y^2) = d/dx (5)

    4x^3 + (this is where I get messed up)


    is it (3x^2)(3y^2 dy/dx) + (y^3)(6x)???
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