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

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

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

If sec((x+y)/(x-y))=a , prove that (dy)/(dx)=y/x .

If x y=1 , prove that (dy)/(dx)+y^2=0 .

If y= (x)/( x+a) , prove that x (dy)/( dx) = y(1-y) .

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

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

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

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

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

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

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If xsin(a+y)+sinacos(a+y)=0 , prove that (dy)/(dx)=(s in^2(a+y))/(sina...

    Text Solution

    |

  2. If (sinx)^y=x+y , prove that (dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsinx-1)

    Text Solution

    |

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

    Text Solution

    |

  4. If y=xsiny , prove that (dy)/(dx)=y/(x(1-xcosy))

    Text Solution

    |

  5. Find the derivative of the function f(x) given by f(x)=(1+x)(1+x^2)...

    Text Solution

    |

  6. If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)...

    Text Solution

    |

  7. If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx

    Text Solution

    |

  8. If x y=e^(x-y) , find (dy)/(dx) .

    Text Solution

    |

  9. If y^x+x^y+x^x=a^b , find (dy)/(dx) .

    Text Solution

    |

  10. If (cosx)^y=(cosy)^x find (dy)/(dx) .

    Text Solution

    |

  11. If cosy=xcos(a+y) , where cosa!=-1 , prove that (dy)/(dx)=(cos^2(a+y))...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If y=x^(tanx)+sqrt((x^2+1)/2) , find (dy)/(dx)

    Text Solution

    |

  15. If y=1+alpha/((1/x-alpha))+(beta//x)/((1/x-alpha)(1/x-beta))+(gamma//...

    Text Solution

    |

  16. If y=x^x , find (dy)/(dx) .

    Text Solution

    |

  17. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(d...

    Text Solution

    |

  18. "If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y...

    Text Solution

    |

  19. If y=e^(x+e^(x+e^(x+dotto\ oo))) , show that (dy)/(dx)=y/(1-y) .

    Text Solution

    |

  20. If y=sqrt(x)^(sqrt(x)^(sqrt(x)^dotoo)) , show that (dy)/(dx)=(y^2)/(x(...

    Text Solution

    |