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If y = { sin "" (x)/(2) sin "" (x ^(2))/...

If `y = { sin "" (x)/(2) sin "" (x ^(2))/(2 ^(2)) . sin "" (x ^(3))/(2 ^(3)).....sin "" (x ^(n))/(2 ^(n))}` then `(dy)/(dx)=`

A

`y ((1)/(2)) tan "" x/2 +tan "" ( x ^(2))/( 2 ^(2)) +....+ (n x ^(n-1))/(x ^(n))tan "" (x ^(n))/(2 ^(n))`

B

`((1)/(2)) tan "" x/2 + ((x)/(2)) tan "" (x ^(2))/(2 ^(2)) + ....+ (nx ^(n-1))/(2 ^(n))tan "" (x ^(n))/(2 ^(n))`

C

`y { ((1)/(2)) cot "" x /2 + ((x)/(2)) cot "" (x ^(2))/( 2 ^(2)) +_ .....+ ((n x ^(n -1))/(2 ^(n)))cot "" (x ^(n))/(2 ^(n))}`

D

`((1)/(2) ) cot "" (x)/(2) ((x)/(2)) cot "" x/2 + ....+ (nx ^(n-1))/(2 ^(n)) cot "" (x ^(n))/(2 ^(n))`

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1B
  1. If (cos x ) ^(y) = (sin y) ^(x) then (dy)/(dx)=

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

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

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

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

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  6. If y = (sin x) ^((sin x) ^((sin x) ^(...oo))), then (dy)/(dx)=

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  7. If y = e ^(x + e ^(x + e^(x ...oo))), then (dy)/(dx)=

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  8. If x = e ^(y+ e ^(y +...10oo)), x gt 0, then (dy)/(dx) is

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  9. If y = x + (1)/(x + (1)/( x +...oo)) then (dy)/(dx) =

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  10. If y = sqrtx ^(sqrtx^(sqrtx^(...oo))), then (dy)/(dx) =

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  11. If y = a ^(x ^(a^(x ^(a ^(x ...oo))))) then (dy)/(dx)=

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

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  13. If x lt 1, then 1/(x + 1) + (2x)/(1 +x^2) + (4x^3)/(1 + x^4) + ….oo =

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  14. If lt 1 then (1-2x)/(1 - x x ^(2)) + ( 2x - 4x ^(3))/(1 - x ^(2) + x ...

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  15. If f (x ) =x ^(2) + (x ^(2))/((1 + x ^(2))) + (x ^(2))/( (1 + x ^(2)))...

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  16. f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan...

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  17. If y = { sin "" (x)/(2) sin "" (x ^(2))/(2 ^(2)) . sin "" (x ^(3))/(2 ...

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  18. If cos ""x/2cos "" (x )/(2 ^(2)) ….cos "" (x)/(2 ^(n)) = (sin x)/( 2 ^...

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  19. If sintheta sin(2alpha+theta)sin(4alpha + theta)...sin(2(n-1)alpha+the...

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  20. If Y = "tan"^(-1)((1)/(1 + x + x^2)) + "tan"^(-1) (1/(x^2 + 3x + 3)) +...

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