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)`

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

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

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

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

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

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

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

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

If x^x+y^x=1 , prove that (dy)/(dx)=-{(x^x(1+logx)+y^x. logy)/(x . y^((x-1)))}

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

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y^(x)=e^(y-x), then prove that (dy)/(dx) = ((1+logy)^(2))/(logy)

    Text Solution

    |

  2. If y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1 then (y prim...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If (sin"x")^y=x+y ,p rov et h a t(dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsin...

    Text Solution

    |

  7. Differentiate: (logx)^x+x^(logx)w i t hr e s p e c t to x :

    Text Solution

    |

  8. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3)) with respec...

    Text Solution

    |

  9. Differentiate the following functions with respect to x : (cos"x")^x ...

    Text Solution

    |

  10. Differentiate the following functions with respect to x : (i) (x^x...

    Text Solution

    |

  11. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),f...

    Text Solution

    |

  12. If sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1...

    Text Solution

    |

  13. If y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt...

    Text Solution

    |

  14. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),p rov et h a t(dy)/(dx)=sqrt((1-y^2...

    Text Solution

    |

  15. if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2 + 1/t^2 then prove that dy/dx...

    Text Solution

    |

  16. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  17. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

    Text Solution

    |

  18. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

    Text Solution

    |

  19. Differentiate the functions with respect to x : tan^(-1){(sqrt(1+a^2x...

    Text Solution

    |

  20. Differentiate the functions with respect to x : cos^(-1){(cosx+sinx...

    Text Solution

    |