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Math Help - is this correct, second-order partial derivatives

  1. #1
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    is this correct, second-order partial derivatives

    Find the first- and second-order derivatives of the following functions:

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

    y=(2x+1)(4x-2)

    y=(x^2+2)^2

    Find all the first-order and second-order partial derivatives of the following functions:

    z=3x^2-2y^4

    z=2xy^2+0.5x^2

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

    this is what i have been able to do i just wanted someone to check if its correct

    y=2x^3+4x^2-x+5
    dy/dx = 6x^2+8x-1

    y=(2x+1)(4x-2)
    dy/dx = (2) (4x-2)+(2x+1)(4)
    dy/dx = 8x-4+8x+4
    dy/dx=16x

    y=(x^2+2)^2
    dy/dx = 2(x^2+2) (2x)
    dy/dx = (2x^2+4)(2x)
    dy/dx = 4x^3+8x

    z=3x^2-2y^4
    ∂z/∂x = 6x
    ∂^z/∂x^2 = 6

    ∂z/∂y = -8y^3
    ∂^2z/∂y^2 = -8(3y^2) = -24y^2

    z=2xy^2+0.5x^2
    ∂z/∂x = 2y^2+0.5(2x) = 2y^2+x
    ∂^2z/∂x^2 = 1
    ∂z/∂y = 2x(2y) = 4xy
    ∂^2z/∂y^2 = 4x

    z=y^3+2x^2 y^2-4x+2
    ∂z/∂x = 2y^2 (2x) - 4 = 4xy^2-4
    ∂^2z/∂x^2 =4y^2
    ∂z/∂y = 3y^2+2x^2(2y) = 3y^2+4x^2y
    ∂^2z/∂y^2 = 3(2y)+4x^2 = 6y+4x^2

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  2. #2
    Senior Member yeKciM's Avatar
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    Smile

    lol it's ok
    but for simple things u can download "microsoft math 3.0." so u can check ur work
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  3. #3
    A Plied Mathematician
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    For completeness, you should compute the mixed partial derivatives, such as \frac{\partial^{2}z}{\partial x\,\partial y}, etc.
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