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)