Home
Class 12
MATHS
If y=(logx)/x , show that (d^2y)/(dx^2)=...

If `y=(logx)/x` , show that `(d^2y)/(dx^2)=(2logx-3)/(x^3)` .

Text Solution

AI Generated Solution

To show that \(\frac{d^2y}{dx^2} = \frac{2 \log x - 3}{x^3}\) for \(y = \frac{\log x}{x}\), we will follow these steps: ### Step 1: Differentiate \(y\) to find \(y'\) Given: \[ y = \frac{\log x}{x} \] ...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos
  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=(log x)/(x), show that(d^(2)y)/(dx^(2))=(2log x-3)/(x^(3))

(d)/(dx)((logx)/(x^(2)))=

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

x(dy)/(dx)=y(logy-logx+1)

If y= (log x) ^(logx) ,then (dy)/(dx)=

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

x (dy)/(dx) + y = x logx

"If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))", show that "(2y-1).(dy)/(dx)=(1)/(x).

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

If y = (e^x logx)/x^2 then (dy)/(dx)

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

    Text Solution

    |

  2. If y=2sinx+3cosx , show that (d^2y)/(dx^2)+y=0 .

    Text Solution

    |

  3. If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .

    Text Solution

    |

  4. If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y...

    Text Solution

    |

  5. If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove t...

    Text Solution

    |

  6. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

    Text Solution

    |

  7. If x=acostheta , y=bsintheta , show that (d^2y)/(dx^2)=-(b^4)/(a^2y^3)...

    Text Solution

    |

  8. If x=a(1-cos^3theta) , y=a\ s in^3theta , prove that (d^2y)/(dx^2)=(32...

    Text Solution

    |

  9. If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a...

    Text Solution

    |

  10. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

    Text Solution

    |

  11. If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1...

    Text Solution

    |

  12. If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-...

    Text Solution

    |

  13. If x=costheta , y=sin^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))...

    Text Solution

    |

  14. If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...

    Text Solution

    |

  15. If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/...

    Text Solution

    |

  16. If y=(sin^(-1)x)^2 , prove that (1-x^2)y2-x y1-2=0 .

    Text Solution

    |

  17. If y=e^tan^((-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

    Text Solution

    |

  18. If y=3cos(logx)+4sin(logx),\ prove that x^2y2+x\ y1+y=0 .

    Text Solution

    |

  19. If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .

    Text Solution

    |

  20. If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .

    Text Solution

    |