Home
Class 12
MATHS
If xy log(x + y) = 1, then prove that ...

If `xy log(x + y) = 1`, then prove that
`(dy)/(dx) = -(y(x^(2)y + x + y))/(x(xy^(2) + x + y))`.

Promotional Banner

Topper's Solved these Questions

  • VERY SIMILAR TEST 9

    ARIHANT PRAKASHAN|Exercise Section C|24 Videos

  • VERY SIMILAR TEST 9

    ARIHANT PRAKASHAN|Exercise Section C|24 Videos

  • VERY SIMILAR TEST 8

    ARIHANT PRAKASHAN|Exercise Section C|25 Videos

Similar Questions

Explore conceptually related problems

If (x)/(x-y)=log((a)/(x-y)) , then prove that (dy)/(dx)=2-(x)/(y) .

If (x-y)*e^((x)/(x-y))=a , then prove that y(dy)/(dx)+x=2y .

If x^(p)y^(q)=(x+y)^(p+q) , then prove that (dy)/(dx)=(y)/(x) .

If y^(x)=e^(y-x) , then prove that (dy)/(dx)=((1+log y)^(2))/(logy) .

If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

Prove that y=tan(x+y) , then (dy)/(dx)=(1+y^(2))/(-y^(2))

If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y .

ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section B
  1. Using differentials, find the approximate value of (3.68)^(3//2).

    Text Solution

    |

  2. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

    Text Solution

    |

  3. If xy log(x + y) = 1, then prove that (dy)/(dx) = -(y(x^(2)y + x +...

    Text Solution

    |

  4. If sin 2x = (2t)/(1 + t^(2)), tan y = (2t)/(1 - t^(2)) then find (dy)/...

    Text Solution

    |

  5. Solve (dy)/(dx) + y = cosx - sinx.

    Text Solution

    |

  6. Find the equation of the curve passing through the point (1, 1) whose ...

    Text Solution

    |

  7. Evaluate int(x^(2))/(x^(4)-x^(2)+12)dx.

    Text Solution

    |

  8. Evaluate the following integrals : Evaluate int(0)^(pi//2)(xsinxcosx...

    Text Solution

    |

  9. Find the area bounded by the curve y = x abs(x), X-axis and ordinates ...

    Text Solution

    |

  10. The plane lx+my=0 is rotated about its line of intersection with the p...

    Text Solution

    |

  11. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin an...

    Text Solution

    |

  12. Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * v...

    Text Solution

    |

  13. Find the vector equation of a plane which is at a distance of 6 units ...

    Text Solution

    |

  14. If sin{cot^(-1)(x + 1)} = cos(tan^(-1)x), then find x.

    Text Solution

    |

  15. One kind of cake requires 200 g of flour and 25 g of fat and another k...

    Text Solution

    |

  16. Consider f:R(+) to [-5, oo) given by f(x)=9x^(2)+6x-5. Show that f i...

    Text Solution

    |

  17. Let R be a relation on the set A of ordered pairs of positive integers...

    Text Solution

    |

  18. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

    Text Solution

    |

  19. Two persons A and B throw a die alternately till one of them gets a th...

    Text Solution

    |

  20. A = [(1, 0), (0, 1)], B = [(1, 0), (0, -1)] and C = [(0, 1), (1, 0)], ...

    Text Solution

    |