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The derivative of Tan ^(-1)"" (sqrt(1 + ...

The derivative of `Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1) "" (2x sqrt(1-x ^(2)))/(1 - 2 x ^(2))at x =0` is

A

1

B

`1//2`

C

`1//4`

D

`1//8`

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1B
  1. The derivative of Cos ^(-1) (2x ^(2) -1) w.r.t. Cos ^(-1) x is

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  2. The derivative of Sec ^(-1)"" (1)/( 2x ^(2) -1) w.r.t . sqrt(1+ 3x ) a...

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  3. The derivative of Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1...

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  4. The derivative of Sin ^(-1) (3x -4x^(3)) w.r.t. Tan ^(-1)"" (x )/( sqr...

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  5. If y = sqrt(sin x + y ) then (dy)/(dx) =

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  6. If y = sqrt( cos x + y) thnd (dy)/(dx) =

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  7. If sin y = x sin (alpha + y) then (dy)/(dx) =

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  8. If cos y =x cos (a + y) then (dy)/(dx)=

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  9. If Cos ^(-1) (( x ^(2) - y ^(2))/(x ^(2) + y ^(2)))=k (a constnat), th...

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

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

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  12. If y= x ^(y) then (dy)/(dx) =

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  13. If x ^(y) = e ^(x -y) then (dy)/(dx) =

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  14. If x ^(y) = log x then (dy)/(dx) at x =e is

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  15. x ^(y) =y ^(x) implies x ( x-y log x ) (dy)/(dx) =

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  16. (d)/(dx){e ^(x^(e))+ x ^(e^(x)) + e ^(x ^(x))}=

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  17. If (cos x ) ^(y) = (sin y) ^(x) then (dy)/(dx)=

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  18. If y = sqrt(x + sqrt(x + sqrt(x + .....oo)))then (dy)/(dx) =

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  19. If y = sqrt(tan x + sqrt(tan x + sqrt(tan + ....oo))) then (dy)/(dx)=

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  20. If y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ....oo))) then (dy)/(dx)

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