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Question
If v(x, y, z) = x3 + y3 + z3 + 3xyz, Show that `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
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Solution
v(x, y, z) = x3 + y3 + z3 + 3xyz
`(del^2"v")/(delydelz) = del/(dely) [(del"v")/(delz)]`
= `del/(dely) [3z^2 + 3xy]`
= 3x .........(1)
`(del^2"v")/(delzdely) = del/(delz) [(del"v")/(delz)]`
= `del/(delz) [3y^2 + 3xz]`
= 3x .......(2)
From (1) and (2)
⇒ `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
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