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

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- Apr 24th 2007, 02:24 AMdadonpartial diff.
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 - Apr 24th 2007, 04:24 AMSoroban
Hello, dadon!

You're*that*close . . .

Quote:

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

- Apr 24th 2007, 11:05 AMdadon
Thanks Soroban lol.. that was doing my head in this morning..