Home
Class 12
MATHS
If x^m\ y^n=1 , prove that (dy)/(dx)=-(m...

If `x^m\ y^n=1` , prove that `(dy)/(dx)=-(m y)/(n x)`

Text Solution

Verified by Experts

Given that,
`x^m\ y^n=1`
`=>log(x^m\ y^n)=log1`
`=>mlogx+nlogx=0`
`=>d/(dx)(mlogx)+d/(dx)(nlogx)=0`
`=>m*1/x+n*1/y (dy)/(dx)=0`
`=>n/y*(dy)/(dx)=-m/x`
`=>(dy)/(dx)=-(m y)/(n x)`
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

If x^(m)y^(n)=(x+y)^(m+n), prove that (dy)/(dx)=(y)/(x)

If x^(m)y^(n)=(x+y)^(m+n), prove that (dy)/(dx)=(y)/(x)

If x^(m)y^(n)=(x+y)^(m+n) prove that (dy)/(dx)=(y)/(x)

If x^(m)y^(n)=(x+y)^(m+n), prove that (dy)/(dx)=(y)/(x)

If ye^(y)=x, prove that,(dy)/(dx)=(y)/(x(1+y))

x^(m)*y^(n)=(x+y)^(m+n) prove that (dy)/(dx)=(y)/(x)

If x^(m)y^(n)=(x+y)^(m+n), Prove that (dy)/(dx)=(y)/(x)

If x^(m)*y^(n)=(x+y)^(m+n), show that (dy)/(dx)=(y)/(x)

If x^(m)+y^(m)=1 such that (dy)/(dx)=-(x)/(y) , then what should be the value of m?

If x^(m)+y^(m)=1 such that (dy)/(dx)=-(x)/(y) . then what should be the value of m ?

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

    Text Solution

    |

  2. If y^x+x^y=(x+y)^(x+y) find dy/dx

    Text Solution

    |

  3. If x^m\ y^n=1 , prove that (dy)/(dx)=-(m y)/(n x)

    Text Solution

    |

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

    Text Solution

    |

  5. If (sinx)^y=(cosy)^x , prove that (dy)/(dx)=(logcosy-ycotx)/(logsinx+x...

    Text Solution

    |

  6. If (cosx)^y=(tany)^x , prove that (dy)/(dx)=(logtany+ytanx)/(logcosx-x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. If y=xsin(a+y) , prove that (dy)/(dx)=(sin^2(a+y))/(sin(a+y)-y cos\ (a...

    Text Solution

    |

  11. If xsin(a+y)+sinacos(a+y)=0 , prove that (dy)/(dx)=(sin^2(a+y))/(sina)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |