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Question
If U(x, y, z) = `log(x^3 + y^3 + z^3)`, find `(del"U")/(delx) + (del"U")/(dely) + (del"U")/(del"z)`
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Solution
U(x, y, z) = `log(x^3 + y^3 + z^3)`
`(del"U")/(delx) = (3x^2)/(x^3 + y^3 + z^3)`
`(del"U")/(dely) = (3y^2)/(x^3 + y^3 + z^3)`
`(del"U")/(delz) = (3z^2)/(x^3 + y^3 + z^3)`
`(del"U")/(delx) + (del"U")/(dely) + (del"U")/(del"z) = (3(x^2 + y^2 + z^2))/(x^3 + y^3 + z^3`
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