Hey All,
how would you solve the following:
given that Ø = 3x^2 + y^3 + z^4
show that x/2.∂Ø/∂x + y/3.∂Ø/∂y + z/4.∂Ø/∂z = Ø
I have found; ∂Ø/∂x=6x, ∂Ø/∂y=3y^2, ∂Ø/∂z=4z^3
Hello, dadon!
You're that close . . .
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