Home
Class 12
MATHS
The derivative of tan^(-1) [(sqrt(1 + x^...

The derivative of `tan^(-1) [(sqrt(1 + x^(2)) - 1)/(x)]` with respect to `tan^(-1)` x is

A

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

B

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

C

1

D

(1/2)

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos

Similar Questions

Explore conceptually related problems

The derivative of tan^(-1)[(sinx)/(1+cosx)] with respect to tan^(-1)[(cosx)/(1+cosx)] is

If tan^(-1)(sqrt(1+x^(2))-1)/(x)=4 then x equals

The derivative of sec^(-1)[(1)/(2x^(2)-1)] with respect to sqrt(1-x^(2)) at x=1//2 is given by

The derivative of sec^(-1)((1)/(2x^(2)-1)) with respect to sqrt(1-x^(2))at x = (1)/(2) is

"tan"^(-1)1/(sqrt(x^(2)-1))|x|gt1

If "tan"^(-1) (sqrt(1+x^2)-1)/x=4 , then x equals :

HIMALAYA PUBLICATION-DIFFERENTIATION-QUESTION BANK
  1. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)), then (dy)/(dx) is

    Text Solution

    |

  2. If y = sin^(-1) ((1-x^(2))/(1+x^(2))), then dy/dx =

    Text Solution

    |

  3. The derivative of tan^(-1) [(sqrt(1 + x^(2)) - 1)/(x)] with respect to...

    Text Solution

    |

  4. d/dx {cos [2sin^(-1) (cos x)]} =

    Text Solution

    |

  5. If y = tan^(-1)((sin x)/(1+cos x)) find (dy)/(dx).

    Text Solution

    |

  6. Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x), where g(x) is continuous. ...

    Text Solution

    |

  7. Let f and g be differentiable functions such that ("fog")'=I. If g'(a)...

    Text Solution

    |

  8. Let f(x+y) = f(x).f(y), forall, x, y. Suppose f(5) =2, f^(')(0) = 3 th...

    Text Solution

    |

  9. lim(hto0)(cos^(2)(x+h)-cos^(2)x)/(h) is equal to :

    Text Solution

    |

  10. If f(x) is differentiable at x = a then lim(a rarr a) (x f(a) - a f(x)...

    Text Solution

    |

  11. If g(x) = 1/sqrt(9+x^(2) then lim(x rarr 4) ((g(x) - g(4))/(x-4) )=

    Text Solution

    |

  12. Let f be twice differentiable function such that f^('')(x) = -f(x) and...

    Text Solution

    |

  13. If y=e^(-x)(Acosx+Bsinx), then y satisfies :

    Text Solution

    |

  14. If y = e^(2x)(A cos 3x - B sin 3x), then y satisfies

    Text Solution

    |

  15. If y = Ae^(2x) + Be^(-3x), then y satisfies

    Text Solution

    |

  16. If y = 2e^(-x)+3e^(-2x), then y satisfies

    Text Solution

    |

  17. If y = (3x+5)e^(-2x), then y satisfies

    Text Solution

    |

  18. If y = Ae^(-4x) + Be^(4x), then y satisfies

    Text Solution

    |

  19. If x = sqrt((1-t^(2))/(1+t^(2)) and y = (sqrt(1+t^(2))-sqrt(1-t^(2)))...

    Text Solution

    |

  20. If y = x+e^(x), then (d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |