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