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

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`

Text Solution

Verified by Experts

`e^x+e^y=e^(x+y)`
`e^x+e^y frac{dy}{dx}=e^(x+y)(1+frac{dy}{dx})`
`e^x+e^y frac{dy}{dx}=(e^x+e^y)(1+frac{dy}{dx})`
`e^x frac{dy}{dx}+e^y=0`
`frac{dy}{dx}+e^(y-x)=0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

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

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

(dy)/(dx)=2y((e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)))

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

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=x+1/(x+1/(1/(x+))), prove that (dy)/(dx)=y/(2y-x)

    Text Solution

    |

  2. If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(...

    Text Solution

    |

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

    Text Solution

    |

  4. If y=(cosx)^((cosx)^(((cosx)^((...oo)) prove that (dy)/(dx)=-(y^2tanx)...

    Text Solution

    |

  5. If y=sqrt(sinx+y),then find (dy)/(dx)dot

    Text Solution

    |

  6. If y=x^x^x^ddot^((((oo)))), (dy)/(dx)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If (sin"x")^y=(cos"y")^x ,p rov et h a t(dy)/(dx)=(logcosy-ycotx)/(log...

    Text Solution

    |

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

    Text Solution

    |

  11. If y=(a x^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1 find dy/dx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Differentiate: (logx)^x+x^(logx) w i t h respect to x

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |