Home
Class 12
MATHS
If x^(16)y^9=(x^2+y)^(17) , prove that x...

If `x^(16)y^9=(x^2+y)^(17)` , prove that `x(dy)/(dx)=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

x+y(dy/dx)=2y

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

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

If x y=4 , prove that x((dy)/(dx)+y^2)=3y

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

If tan^(-1)((x^2-y^2)/(x^2+y^2))=a , prove that (dy)/(dx)=x/y((1-tana))/((1+tana)) .

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

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

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

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

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=x^(logx)+(logx)^x then find (dy)/(dx)

    Text Solution

    |

  2. If x^(13)y^7=(x+y)^(20) , prove that (dy)/(dx)=y/x

    Text Solution

    |

  3. If x^(16)y^9=(x^2+y)^(17) , prove that x(dy)/(dx)=2y

    Text Solution

    |

  4. If y=sin(x^x) , prove that (dy)/(dx)=cos(x^x) .x^x(1+logx)

    Text Solution

    |

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

    Text Solution

    |

  6. If x^y. y^x=1 , prove that (dy)/(dx)=-(y(y+xlogy))/(x(ylogx+x))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |