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If u= tan^(-1) ((x^(3) + y^(3))/(x-y)), ...

If `u= tan^(-1) ((x^(3) + y^(3))/(x-y))`, Prove that `x(del u)/(del x) + y(del u)/(del y) = sin 2u`.

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Knowledge Check

  • If u=(x-y)^(2) , then (del u)/(del x) + (del u)/(del y) is

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    1
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    `-1`
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  • If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (del u)/(del y)=

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    `u ^(-1)`
    B
    `2u`
    C
    1
    D
    `2u`

  • If z =e^((x +y)/(x -y)) then x (del xz)/(del x) + y (del z)/(dely)=

    A
    2
    B
    0
    C
    1
    D
    `-1`

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    Explore conceptually related problems

    If u(x,y) = (x^(2) + y^(2))/sqrt(x+y) , prove that x(del u)/(del x) + y(del u)/(del y) = 3/2 u .

    If v(x,y) = log((x^(2) +y^(2))/(x+y)) , prove that x(del v)/(del x) + y(del v)/(del y)=1 .

    If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.

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    If f(x,y) =2x^(3) - 11x^(2)y + 3y^(3) , prove that x(del f)/(del x) + y(del f)/(del y)=3f .

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