Home
Class 12
MATHS
If y = tan^(-1)((sqrt(1 + x^2)-1)/(x)), ...

If `y = tan^(-1)((sqrt(1 + x^2)-1)/(x))`, prove that `(dx)/(dy) = 1/(2(1 + x^2))`

Text Solution

Verified by Experts

The correct Answer is:
A
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

If y=tan^(-1)((1+sin x)/(cos x))" shoe that "(dy)/(dx)= (1)/(2) .

If sqrt(1 -x^2) + sqrt(1 - y^2) = a(x - y) prove that (dy)/(dx) = (sqrt(1 - y^2))/(sqrt(1-x^2)) .

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

If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/((1 + x)^(2))

If y = tan^(-1) sqrt((1+sin x)/(1-sinx)) , then dy/dx =

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

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

HIMALAYA PUBLICATION-DIFFERENTIATION-QUESTION BANK
  1. If f(x) = log(a) (log(a)x), then f^(')(x) is

    Text Solution

    |

  2. If f(x) is odd differentiable function defined on (-oo,oo), such that ...

    Text Solution

    |

  3. The differential coefficient of f(log x) w.r.t. x when f(x) = log x

    Text Solution

    |

  4. If y = x^(x)^(x)^(x)^(oo), then x(1-y log x) dy/dx =

    Text Solution

    |

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

    Text Solution

    |

  6. If f(x) = x +2, then f^(')(f(x)) at x = 4 is

    Text Solution

    |

  7. If y = [f(x)}^(phi(x))then dy/dx is

    Text Solution

    |

  8. If y = tan^(-1)((sqrt(1 + x^2)-1)/(x)), prove that (dx)/(dy) = 1/(2(1 ...

    Text Solution

    |

  9. If f(x) = log |x|, x ne 0 then f^(')(x) equals

    Text Solution

    |

  10. If f(x) = x tan^(-1)x, then f^(')(1) is equal to

    Text Solution

    |

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

    Text Solution

    |

  12. If y=x^(x^(x^(x^(x^(oo))))), then x(dy)/(dx) is equal to

    Text Solution

    |

  13. The derivative of log(10)x with respect to x^(2) is

    Text Solution

    |

  14. If y = sin^(-1) (x/2) + cos^(-1) (x/2) then the value of dy/dx is

    Text Solution

    |

  15. If g is the inverse function of f and f^(')(x) = 1/(1+x^(n)), then g^(...

    Text Solution

    |

  16. The derivative of (tan x) w.r.t g(sec x) at x = pi/4 where, f^(')(1) =...

    Text Solution

    |

  17. If y = [log(cosx) (sin x)][log(sinx) cosx]+sin^(-1) ((2x)/(1+x^(2))) t...

    Text Solution

    |

  18. The derivative of tan^(-1) ((2x)/(1-x^(2))) w.r.t sin^(-1) ((2x)/(1+x^...

    Text Solution

    |

  19. If x = a (cos x + log tan theta/2) and y = a sin theta then dy/dx is ...

    Text Solution

    |

  20. If f(x) = 1/(1-x), then the derivative of the composition function f[f...

    Text Solution

    |