Home
Class 12
MATHS
If u = log (x^(3) + y^(3) + z^(3) - 3xyz...

If `u = log (x^(3) + y^(3) + z^(3) - 3xyz)`, then `(x + y + z)(u_(x) + u_(y) + u_(z))` is equal to

A

0

B

x + y + z

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    SIA PUBLICATION|Exercise Problems|48 Videos
  • EAMCET - 2018 (TS) SHIFT - 1

    SIA PUBLICATION|Exercise EXERCISE - Chemistry|8 Videos

Similar Questions

Explore conceptually related problems

If x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz .

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

If x+y+z=0, show that x^3 + y^3+z^3- 3xyz .

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

Factorise 27 x ^(3) + y ^(3) + z ^(3)-9 xyz using identitiy.

If u + iv = (3i)/(x + iy + 2) , then y in terms of u , v is

Do the following Division 8x^(3)y^(3)z^(3) div 16 xyz

Verify that x^3 + y^3 + z^3- 3xyz=1/2 (x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]

If (x+iy)^(3) = u + iy , then show that u/x + v/y = 4(x^(2)-y^(2))

The (x+4)/(3) = (y+6)/(5) = (z-1)/(-2) and 3x - 2y + z+5 =0 = 2x + 3y + 4z -k are coplanar for k is equal to

SIA PUBLICATION-DIFFERENTIATION -Problems
  1. (d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) ...

    Text Solution

    |

  2. Cos^(-1) ((y)/(b)) =2 log "" ((x)/(2)) , x gt 0 implies x ^(2) (a ^(2)...

    Text Solution

    |

  3. If u = log (x^(3) + y^(3) + z^(3) - 3xyz), then (x + y + z)(u(x) + u(y...

    Text Solution

    |

  4. f (x) = log (e ^(x) ((x-2)/(x +2))^(3//4))impliesf'(0)=

    Text Solution

    |

  5. If xy ne 0, x + y ne 0 and x^(m)y^(n) = (x + y)^(m+n), where, m, n ne ...

    Text Solution

    |

  6. x ^(2) + y^(2) = t + 1/t, x ^(4) + y^(4) = t ^(2) + (1)/( t ^(2)) impl...

    Text Solution

    |

  7. If f(x) = (X^(2) -1)^(7), then f^((14))(x) is equal to

    Text Solution

    |

  8. If y = (1 + x) (1 + x^(2)) .. (1 + x^(2n)), then ((dy)/(dx))(x = 0) is...

    Text Solution

    |

  9. If Cos ^(-1) (( x ^(2) - y ^(2))/(x ^(2) + y ^(2)))=k (a constnat), th...

    Text Solution

    |

  10. If f(x) =|x| + |sin x| for x in (-(pi)/(2),(pi)/(2)), then its left h...

    Text Solution

    |

  11. If y = (lot (e) x)/(x) and z = log (e) x, then (d ^(2) y)/(dz^(2)) + ...

    Text Solution

    |

  12. IF f(x) = (cosx)(cos2x)… (cosnx), then f(x)+sum(t prop1)^(1)(rtanrx)f(...

    Text Solution

    |

  13. If y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(2)))+sin^(-1)((2ax)/(a^(2)+x^(...

    Text Solution

    |

  14. f (x) = sin x + cos x implies f ((pi)/(4)) f ^((iv)) ((pi)/(4)) =

    Text Solution

    |

  15. If y = sin(m sin^(-1)x), then (1-x^(2))y(2) - xy(1) is equal to (Here,...

    Text Solution

    |

  16. x = (1-sqrt(y))/(1+sqrt(y)) rArr(dy)/(dx) is equal to

    Text Solution

    |

  17. x = cos^(-1)((1)/(sqrt(1+t^(2)))),y = sin^(-1)((t)/(sqrt(1+t^(2))))rAr...

    Text Solution

    |

  18. (d)/(dx ) [a Tan ^(-1) x + b log ((x-1)/(x +1)) ] = (1)/(x ^(4) - 1) i...

    Text Solution

    |

  19. y=e^(asin^(-1x))rArr(1-x^(2))y(n+2)-(2n+1)xy(n+1) is equal to

    Text Solution

    |

  20. If x = a{costheta + log tan((theta)/(2))} andy = a sin theta, then (dy...

    Text Solution

    |