Home
Class 12
MATHS
If y=tan^(-1)sqrt(x^(2)-1), then the rat...

If `y=tan^(-1)sqrt(x^(2)-1)`, then the ratio `(d^(2)y)/(dx^(2)):(dy)/(dx)=`

A

`(x(x^(2)+1))/(1-2x^(2))`

B

`(1+2x^(2))/(x(x^(2)+1))`

C

`(1-2x^(2))/(x(x^(2)-1))`

D

`(x(x^(2)-1))/(1+2x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise Latest Question from AIEEE/JEE Examinations|7 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Recent competitive Questions|12 Videos

Similar Questions

Explore conceptually related problems

If y=(x+sqrt(1+x^(2)))^(n) , then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx) is

If y = tan^(-1) sqrt((1-cos x)/(1+cosx)) , then (d^(2)y)/(dx^(2)) = =

If e^(y)(x+1)=1 . Show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

y=log_e(tan^(- 1)sqrt(1+x^2)) then dy/dx is

If y = (tan^(-1)x)^(2) then show that (x^(2) + 1)^(2) (d^2 y)/(dx^2) + 2x(x^2 + 1)(dy)/(dx) = 2

If y= ( sin^(-1) x)^(2) , show that (1-x^(2) ) (d^2 y)/( dx^2) - x (dy)/(dx) =2

If y=(sin^(-1)x) . Show that (1-x^(2)) (d^(2)y)/(dx^(2))-x((dy)/(dx))=0

MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -RCQs (Questions from Karnataka CET & COMED)
  1. The drivative of e^(ax)cos bx with rexpect to x is re^(ax)cosbx+"tan"^...

    Text Solution

    |

  2. If x=acos^(3)theta and y=asin^(3)theta, then (dy)/(dx)=

    Text Solution

    |

  3. If y=tan^(-1)sqrt(x^(2)-1), then the ratio (d^(2)y)/(dx^(2)):(dy)/(dx)...

    Text Solution

    |

  4. If sqrt(r ) =ae^(thetacotalpha) where a and alpha are real numbers the...

    Text Solution

    |

  5. The derivative of "tan"^(-1)(sinx)/(1+cosx) w.r.t. "tan"^(-1)(cosx)/(1...

    Text Solution

    |

  6. d/(dx)[cos^(2)(cot^(-1)sqrt((2+x)/(2-x)))]

    Text Solution

    |

  7. If f(x)=((sin^(2)x)/(1+cotx))+(cos^(2)x)/(1+tan), then f'((pi)/(4)) is...

    Text Solution

    |

  8. If cos^(-1)((y)/(b))=nlog((x)/(n)), then :

    Text Solution

    |

  9. f(x)=2a-x in -altxlta=3x-2a in a lex. Then which of the following i...

    Text Solution

    |

  10. If x+y=tan^(-1)y" and "(d^(2)y)/(dx^(2))=f(y)(dy)/(dx), then f(y)=

    Text Solution

    |

  11. Let f(x) = cos^(-1) [(1)/(sqrt13) (2 cos x - 3 sin x)]. Then f(0.5) =

    Text Solution

    |

  12. If y=(1+x)(1+x^(2))(1+x^(4)), then (dy)/(dx) at x=1 is :

    Text Solution

    |

  13. If y = (tan^(-1)x)^(2) then show that (x^(2) + 1)^(2) (d^2 y)/(dx^2) +...

    Text Solution

    |

  14. If the function f(x) defined by f(x)=(x^(100))/(100)+(x^(99))/(99)+....

    Text Solution

    |

  15. Which of the following functions is differentiable at x=0. ?

    Text Solution

    |

  16. If x=a(cost+logtant//2),y=asint, then (dy)/(dx)=

    Text Solution

    |

  17. If f(x)=xtan^(-1)x, then lim(xto1)(f(x)-f(1))/(x-1)=

    Text Solution

    |

  18. If f(y)=f(x^(2)+2) and f'(3)=5, then (dy)/(dx) at x=1 is :

    Text Solution

    |

  19. If x = a cos^(3) theta , y = a sin^(3) theta , then 1+((dy)/(dx))^(2)...

    Text Solution

    |

  20. If the function g(x) is defined by g(x) = (x^(200))/(200) +(x^(199...

    Text Solution

    |