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Math Help - Quicky question about using the Chain Rule

  1. #1
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    Quicky question about using the Chain Rule

    I am curious as to how you would write the derivative when using the chain rule for longer polynomials?

    we learned how to do examples such as y = (5x + 1)^4

    but I am stumped as to how you would write it when the example is per se,
    y = 2(2x + 4(3x + 2)^5 - 5x^2)^4 - 6x

    so for this example, i would get

    y' = 8(2x + 4(3x + 2)^5 - 5x^2)^3 x (the derivative of the stuff inside the bracket "u") - 6

    What i'm wondering is, for the "u" part, how do i write it?

    would I go 2 + 20(3x+2)^4 x 3 - 10x or would i write it such as 2(20(3x+2)^4)(3)(10x) and multiply them all together like that

    thanks for your help
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  2. #2
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    Quote Originally Posted by mneox View Post
    I am curious as to how you would write the derivative when using the chain rule for longer polynomials?

    we learned how to do examples such as y = (5x + 1)^4

    but I am stumped as to how you would write it when the example is per se,
    y = 2(2x + 4(3x + 2)^5 - 5x^2)^4 - 6x

    so for this example, i would get

    y' = 8(2x + 4(3x + 2)^5 - 5x^2)^3 x (the derivative of the stuff inside the bracket "u") - 6

    What i'm wondering is, for the "u" part, how do i write it?

    would I go 2 + 20(3x+2)^4 x 3 - 10x or would i write it such as 2(20(3x+2)^4)(3)(10x) and multiply them all together like that

    thanks for your help
    It is like the first thing you said, (2+20(3x+2)^4(3)-10x) When using chain rule you multiply the first part by the second while still following all the other rules of differentiation.

    Your answer should look like: 8(2x+4(3x+2)^5-5x^2)^3(2+60(3x+2)^4-10x)-6 You should multiply the 8 through the second part as well there to polish it off.
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