Home
Class 12
MATHS
If y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+...

If `y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1)))`, then `(dy)/(dx)=` ……………

A

x

B

`(1)/(x)`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `y=sec^(-1)((sqrt(x)-1)/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x)-1))`
`y=cos^(-1)((x+sqrt(x))/(sqrt(x-1)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1)))`
`y=(pi)/(2)[becausesin^(-1)x+cos^(-1)x=(pi)/(2)]`
`therefore(dy)/(dx)=0`
Hence the correct answer from the given alternative is .
Promotional Banner

Topper's Solved these Questions

  • OCTOBER 2015

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION -II|20 Videos

  • OCTOBER 2014

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION - II|19 Videos

Similar Questions

Explore conceptually related problems

If y = sec^(-1)((sqrtx-1)/(x+sqrt(3)))+ sin^(-1)((x+sqrt(3))/(sqrt(x)-1)) then find dy/dx

If y=sqrt(x)+(1)/(sqrt(x)) , then (dy)/(dx)=

If y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1)) then (dy)/(dx) is equal to?

If y= sqrt(x-1) +sqrt( x+1) ,then (dy)/(dx)

Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))

If y=sqrt((a-x)(x-b))-(a-b)tan^(-1)((sqrt(a-x))/(sqrt(x-b))) then (dy)/(dx)=

If y=sqrt((sqrt(x-1))/(sqrt(x+1)))," then "(dy)/(dx)|_(x=4)=

If y= (sqrt( x) +(1)/(sqrt(x)) ) ^(5) , then (dy)/(dx) =

GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- OCTOBER 2015-SECTION -II
  1. If y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1...

    Text Solution

    |

  2. If I=int(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx, then the val...

    Text Solution

    |

  3. The solution of the differential equation (dy)/(dx)=secx-ytanx is :

    Text Solution

    |

  4. Evaluate : int(1)/(xlogxlog(logx))dx

    Text Solution

    |

  5. Find the area of the parabola y^2=4a xbounded by its latus rectum.

    Text Solution

    |

  6. Find k ,such that the function P(x)={{:(k({:(4),(x):}),,x=0","1"...

    Text Solution

    |

  7. Given X~B(n,p).If E(X)=6 and Var (X) = 4.2, find the value of n.

    Text Solution

    |

  8. Solve the different equation y-x(dy)/(dx)=0.

    Text Solution

    |

  9. Discuss the continuity of the following functions at the points shown ...

    Text Solution

    |

  10. If f'(x)=k(cos x-sinx), f'(0)=3, f((pi)/(2))=15, find f(x)

    Text Solution

    |

  11. cos^(-1)((3cosx-2sinx)/(sqrt(13)))

    Text Solution

    |

  12. Show that int(1)/(x^(2)sqrt(a^(2)+x^(2)))dx=(-1)/(a^(2))(sqrt(a^(2)+x...

    Text Solution

    |

  13. A rectangle has an area of 50 "cm"^(2). Find its dimensions for least ...

    Text Solution

    |

  14. int(-a)^(a)f(x)dx= 2int(0)^(a)f(x)dx, if f is an even function 0, if...

    Text Solution

    |

  15. If y =f(u) is differentiable function of u, and u=g(x) is a differenti...

    Text Solution

    |

  16. Each of the total fice questions in amultiple choice examination has f...

    Text Solution

    |

  17. If f(x)=x^(2)+a, for xge0, f(x)=2sqrt(x^(2)+1)+b,"for"xlt0andf((1)/(2...

    Text Solution

    |

  18. Find the approximate values of : cos(89^(@)30)," given "1^(@)=0.0175...

    Text Solution

    |

  19. Solve the different equation : x+y(dy)/(dx)=sec(x^(2)+y^(2)). Also f...

    Text Solution

    |

  20. Find the expected value ,variance and standard deviation of random var...

    Text Solution

    |