Second Partial Derivatives of v = e^(6xe^y)?

v = e^(6xe^y) I have to find the first and second derivatives with respect to xx, xy, yx, and yy. I just can't for the life of me remember how to do it. I have the answers here just need the work for one or two of them so I can practice

Comments

  • ohms law should help

  • xx

    36 e^(6 e^y x + 2 y)

    yy

    6 e^(6 e^y x + y) x (1 + 6 e^y x)

    xy

    6 e^(6 e^y x + y) (1 + 6 e^y x)

    yx

    6 e^(6 e^y x + y) (1 + 6 e^y x)

  • v = e^(6xe^y)

    ∂v/∂x = e^(6xe^y) (6e^y)

    ∂v/∂x = 6 e^y e^(6xe^y) ----------(1)

    ∂v/∂y = e^(6xe^y) 6xe^y

    ∂v/∂y = 6x e^y e^(6xe^y) ------------(2)

    xx = ∂^2v/∂x^2 = differentiate (1) with respect to x only (y is a constant)

    = 6e^y e^(6xe^y) [6e^y]

    = 36 e^(2y) e^(6xe^y)

    xy = ∂^2v/∂x∂y = differentiate (1) with respect to y only ( x is a constant)

    = 6 e^y e^(6xe^y) + 6 e^y e^(6xe^y) [6xe^y]

    = 6 e^y e^(6xe^y) + 36 e^(2y) e^(6xe^y)

    yy = ∂^2v/∂y^2 = differentiate (2) with respect to y only (x is a constant)

    = 6x e^y e^(6xe^y) + 6x e^y e^(6xe^y) [6xe^y]

    = 6x e^y e^(6xe^y) + 36 x e^(2y) e^(6xe^y)

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