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

If `y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0.` Find `(dy)/(dx)dot`

A

1

B

0

C

`(x-1)/(x+1)`

D

`(x+1)/(x-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that
`sin^(-1)x+cos^(-1)x=(pi)/(2)`
`becausey=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1))`
`=cos^(-1)((x-1)/(x+1))+sin^(-1)((x-1)/(x+1))`
`=(pi)/(2)`
On differentiating w.r.t. x, we get
`(dy)/(dx)=0`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 04

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHMATICS)|50 Videos

  • PRACTICE SET 06

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

Similar Questions

Explore conceptually related problems

Ify=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)), then (dy)/(dx)

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

If y=tan^(-1)((1-x)/(1+x)), find (dy)/(dx)

if y=cos^(-1)((1-x)/(1+x)) then find (dy)/(dx)

If y=sin^(-1)(3x)+sec^(-1)((1)/(3x)), find (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=sin^(-1)((1-x^(2))/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2))) find (dy)/(dx)

If y=sec^(-1) ((sqrtx-1)/(x+sqrtx))+sin^(-1) ((x+sqrtx)/(sqrtx-1))," then " (dy)/(dx)=

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 05-Paper 2 (Mathematics)
  1. The function f(x)=2x^3-15 x^2+36 x+4 is maximum at x= (a) 3 (b) 0 (c)...

    Text Solution

    |

  2. lim(x to 0) ((4^(x)-9^(x))/((4^(x)+9^(x)))) is equal to

    Text Solution

    |

  3. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

    Text Solution

    |

  4. lim(x to 0) ((1+logx-x)/(1-2x+x^(2)) is equal to

    Text Solution

    |

  5. Let f(x)={{:(0,x lt 0),(x^(2),xge0):}, then for all values of x

    Text Solution

    |

  6. For a random variable X, E(X)=3 and E(X^2)=11 Then, variance of X is

    Text Solution

    |

  7. int0^pix/(a^2cos^2x+b^2sin^2x)dx

    Text Solution

    |

  8. If (d^(2)y)/(dx^(2))+sinx=0, then the solution of differential equatio...

    Text Solution

    |

  9. int(a^(x//2))/(sqrt(a^(-x)-a^(x)))dx is equal to

    Text Solution

    |

  10. if x=loge t , t > 0 and y+1=t^2 then (d^2y)/(dx^2)

    Text Solution

    |

  11. The line perpendicular to the plane 2x-y+5z=4 passing through the poin...

    Text Solution

    |

  12. If in DeltaABC, a=2b and A=3B, then A is equal to

    Text Solution

    |

  13. cot^(-1)((alpha)/(2))-tan^(-1)(sqrt(cosalpha))=x, then sin x is equal ...

    Text Solution

    |

  14. The solution of differential equation (1+x)ydx+(1-y)xdy=0 is

    Text Solution

    |

  15. If int(log" "2)^(x)(du)/((e^(u)-1)^(1//2))=(pi)/(6), then e^(x) is equ...

    Text Solution

    |

  16. If tangent tto the curve x=at^(2),y=2at is perpendicular to X-axis, th...

    Text Solution

    |

  17. Three numbers are chosen from 1 to 20. Find the probability that they ...

    Text Solution

    |

  18. The general solution of |sinx|=cosx is (When ninz) given by

    Text Solution

    |

  19. The equation of the tangent from the point (0, 1) to the circle x^2+y^...

    Text Solution

    |

  20. The sum of first 8 terms of the geometric series 2+6+18+54+ . . . Is

    Text Solution

    |