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Math Help - Differentiate by definition - please help

  1. #1
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    Differentiate by definition - please help

    Can someone confirm I have done this correctly?

    Y = 3x^4 + 2x^3 + 4x at P (x, y), let Q (X + Δx, y+Δy)
    lim(Δx->0)
    3(x+Δx)^4 + 2(x+Δx)^3 + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
    Δx=lim(Δx->0)
    3(x^4 + 4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(x^3 + 3x^2Δx + 3xΔx^2 + Δx^3) + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
    Δx= lim(Δx->0)
    3(4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(3x^2Δx + 3xΔx^2 + Δx^3) + 4(Δx)
    lim(Δx->0) 3(4x^3+ 6x^2Δx + 4xΔx^2) + 2(3x^2 + 3xΔx + Δx^2) + 4(1)
    3(4x^3) + 2(3x^2) + 4(1)

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  2. #2
    Member dokrbb's Avatar
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    Re: Differentiate by definition - please help

    Quote Originally Posted by calcnewby View Post
    Can someone confirm I have done this correctly?

    Y = 3x^4 + 2x^3 + 4x at P (x, y), let Q (X + Δx, y+Δy)
    lim(Δx->0)
    3(x+Δx)^4 + 2(x+Δx)^3 + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
    Δx=lim(Δx->0)
    3(x^4 + 4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(x^3 + 3x^2Δx + 3xΔx^2 + Δx^3) + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
    Δx= lim(Δx->0)
    3(4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(3x^2Δx + 3xΔx^2 + Δx^3) + 4(Δx)
    lim(Δx->0) 3(4x^3+ 6x^2Δx + 4xΔx^2) + 2(3x^2 + 3xΔx + Δx^2) + 4(1)
    3(4x^3) + 2(3x^2) + 4(1)

    That's right - You can actually do it by yourself, taking the derivative

    y'=
    4*3x^3 + 3*2x^2+ 4*1
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