Home
Class 12
MATHS
If x=e^(x//y), prove that (dy)/(dx)=(x-y...

If `x=e^(x//y)`, prove that `(dy)/(dx)=(x-y)/(xlogx)`.

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 5

    ARIHANT PUBLICATION|Exercise Long answer type question|13 Videos
  • SAMPLE PAPER 5

    ARIHANT PUBLICATION|Exercise Long answer type question|13 Videos
  • SAMPLE PAPER 4

    ARIHANT PUBLICATION|Exercise Long Answer Type Questions|13 Videos
  • THREE-DIMENSIONAL GEOMETRY

    ARIHANT PUBLICATION|Exercise Chapter Practice|34 Videos

Similar Questions

Explore conceptually related problems

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

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

If x=e^(cos2t) and y=e^(sin2t) , then prove that (dy)/(dx)=(-ylogx)/(x logy) .

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

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

Solve (dy)/(dx)+y=e^(-x)

IF x^y=e^(x-y) then show that (dy)/(dx)=(logx)/[log(xe)]^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 .

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

ARIHANT PUBLICATION-SAMPLE PAPER 5-Short answer type question
  1. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

    Text Solution

    |

  2. A bag contains 5 red marbles and 3 black marbles. Three , marbles are ...

    Text Solution

    |

  3. Using properties of determinants prove that |{:(a^2+2a,2a+1,1),(2a+1...

    Text Solution

    |

  4. A and B throw a pair of dice alternately. A wins the game, if he gets ...

    Text Solution

    |

  5. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),(7,8):}], find a matrix C such ...

    Text Solution

    |

  6. Find the derivative of cos^(-1)((sin x +cos x)/(sqrt(2))),(-pi)/(4)lt ...

    Text Solution

    |

  7. If x=e^(x//y), prove that (dy)/(dx)=(x-y)/(xlogx).

    Text Solution

    |

  8. Find the condition that curves 2x = y^(2) and 2xy = k intersect ortho...

    Text Solution

    |

  9. Evaluate int(1)^(3) (3x^(2) + 2x+1) dx .

    Text Solution

    |

  10. Examine the differentiability of the function f defined by f(x)={{:(2x...

    Text Solution

    |

  11. Evaluate intsqrt((1+x)/(1-x))dx, x ne 1

    Text Solution

    |

  12. Solve the following differential equation x^(2).(dy)/(dx)-xy=1+cos((...

    Text Solution

    |

  13. Find the area of region enclosed by the curve x=3cost, y=2sint.

    Text Solution

    |

  14. int0^(pi/2) (sin^2xdx)/(sinx+cosx)

    Text Solution

    |

  15. Form the differential equation having y= (sin^(-1)x)^(2)+A cos^(-1)x+B...

    Text Solution

    |

  16. The two vectors hatj+hatk and 3hati+hatj+4hatk represents the two side...

    Text Solution

    |

  17. If vec(a) = hat(i) + 4hat(j) + 2hat(k), vec(b) = 3hat(i) - 2hat(j) + 7...

    Text Solution

    |

  18. Find the co-ordinates of the point where the line joining (3,4,-5) and...

    Text Solution

    |

  19. The vectors from origin to the points A and B are A=2hati-3hatj+2hatk ...

    Text Solution

    |

  20. For any vector a , show that a=(a*hati)hati+(a*hatj)hatj+(a*hatk)hat...

    Text Solution

    |