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))`

Answer

Step by step text solution for If y = tan^(-1)((sqrt(1 + x^2)-1)/(x)), prove that (dx)/(dy) = 1/(2(1 + x^2)) by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    SUBHASH PUBLICATION|Exercise FOUR MARKS QUESTIONS WITH ANSWERS|10 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    SUBHASH PUBLICATION|Exercise FIVE MARKS QUESTIONS WITH ANSWERS|15 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    SUBHASH PUBLICATION|Exercise TWO MARKS QUESTIONS WITH ANSWERS|26 Videos
  • CONSTRUCTIONS

    SUBHASH PUBLICATION|Exercise QUESTION|1 Videos
  • DETERMINANT

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|10 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)) .

Knowledge Check

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

    A
    (1/2)
    B
    1/(cosx)
    C
    0
    D
    1
  • If y = tan^(-1) ((x-sqrt(1-x^(2)))/(x+sqrt(1-x^(2)))) , then dy/dx =

    A
    `1/(1-x^(2))`
    B
    `1/(sqrt(1-x^(2))`
    C
    `1/(1+x^(2))`
    D
    `1/(sqrt(1+x^(2))`
  • If y = tan^(-1) sqrt((1+sin x)/(1-sinx)) , then dy/dx =

    A
    1
    B
    (-1/2)
    C
    (1/2)
    D
    0
  • Similar Questions

    Explore conceptually related problems

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

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

    If y = tan^(-1) ((sqrt(1+x) +sqrt(1-x))/2) 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)=