Home
Class 11
MATHS
(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ ...

`(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=`

Text Solution

Verified by Experts

The correct Answer is:
`(-x)/( sqrt (1 - x ^(4)))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    AAKASH SERIES|Exercise SOLVED EXAMPLES |20 Videos

  • DIFFERENTIATION

    AAKASH SERIES|Exercise ADVANCED ANALYTICAL SOLVED EXAMPLES |6 Videos

  • CONTINUITY

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|34 Videos

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (PRACTICE SHEET (ADVANCED)) (Integer Type Questions)|5 Videos

Similar Questions

Explore conceptually related problems

(d)/(dx) {Tan ^(-1) ""(2x)/(1- x ^(2))}=

(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=

(d)/(dx) {Tan ^(-1) ""(sqrt (( x ^(2))/(a ^(2) -x ^(2))))}=

(d)/(dx) {Tan ^(-1) ""(sqrt(1-x))/(1+ x) }=

(d)/(dx) {Sin ^(-1) ""(sqrt((1-x)/2)}=

(d)/(dx) {Cos ^(-1) ""(sqrt((1 + x)/2))}=

int (sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(4)))dx=

(d)/(dx) {Tan ^(-1) "" sqrt([(x)/(1-x)])}=

(d)/(dx) {Tan ^(-1) ((b tan x )/(a ))}=

(d)/(dx) {Tan ^(-1) ((x-a)/(1 + ax ))}=

AAKASH SERIES-DIFFERENTIATION -ADVANCED SUBJECTIVE TYPE QUESTIONS
  1. (d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^...

    Text Solution

    |

  2. Let f : R to R ,f (a) =1, f '(a) = 2 then prove that Lt (x to 0) ((...

    Text Solution

    |

  3. Let f be twice differentiable function such that f^11(x) = -f(x) "and ...

    Text Solution

    |

  4. If f: R to R is defined by f(x) =x+ sqrt(x^(2)), then f is:

    Text Solution

    |

  5. Let f ((x + y )/( 2)) = (f (x) + f (y))/( 2) AA x,y,in R. If f (0) =1....

    Text Solution

    |

  6. If f ((x + 2y)/(3)) = (f (x) + 2f (y))/( 3) AA x, y in R and f '(0) = ...

    Text Solution

    |

  7. If f ((x+ y)/( 3)) = (2 + f (x) + f (y))/(3) AA x, y in R and f'(2) =2...

    Text Solution

    |

  8. The number of cirtical points of the function f(x)=|x|e^(-x) must be

    Text Solution

    |

  9. If f (x-y), f (x) ,f (y) and f (x + y) are in A.P for all x,y in E an...

    Text Solution

    |

  10. Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f ...

    Text Solution

    |

  11. If f (x +y) = 2 f (x) .f(y) such that f '(0) 3 and (4) = 2 find d'(4)...

    Text Solution

    |

  12. Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x,...

    Text Solution

    |

  13. If f (x) is a function such that (x - y) f (x + y)- (x + y) f (x - y) ...

    Text Solution

    |

  14. Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(...

    Text Solution

    |

  15. If f (x) = {{:((x ^(2))/( 2 ) "," , 0 le x lt 1), (2x ^(2) - 3x + (3)/...

    Text Solution

    |

  16. Show that the function f (x) = |x-1|+ | x- 2| is not differentiable at...

    Text Solution

    |

  17. Prove theat the greatest interger function defined by f(x)= |x|, 0 lt ...

    Text Solution

    |

  18. Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x...

    Text Solution

    |

  19. If 'f is a function such that f (x + y) =f (x) f (y) for all x,y in R ...

    Text Solution

    |

  20. If f (x) = ax ^(2) + bx + c then find Lt (x to 5) (f (x) - f (5))/(x-...

    Text Solution

    |

  21. If f (x) has a derivative at x =a then find Lt (x to a) (x f (a) - a f...

    Text Solution

    |