Hello, dadon!

You'rethatclose . . .

Given: .F .= .3x² + y³ + z^4 .[1]

show that: .(x/2)·(∂F/∂x) + (y/3)·(∂F/∂y) + (z/4)·(∂F/∂z) .= .F .[2]

I have found: .∂F/∂x = 6x, .∂F/∂y = 3y², .∂F/∂z = 4z³

Substitute your findings into the left side of [2]:

. . (x/2)·(6x) + (y/3)·(3y²) + (z/4)·(4x³)

. . = .3x² + y³ + z^4

. . . . \___________/ . . . . . Q.E.D.

. . . . From [1], this is F