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If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dot...

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo)))` , prove that `(dy)/(dx)=(cosx)/(2y-1)`

A

` (cos x) /( 1-2y ) `

B

` (cos x) /( 2y -1) `

C

` (2cos x)/( 1-2y )`

D

` (2cos x)/( 2y -1)`

Text Solution

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The correct Answer is:
B
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NIKITA PUBLICATION-DIFFERENTIATION -MCQ
  1. If log (10) ((x^(2) - y^(2))/(x^(2) + y^(2))) = 2 , " then" (dy)/(dx)...

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  2. IF log (10)""((x^(3)-y^(3))/(x^(3)+y^(3)))=2 then (dy)/(dx)=

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  3. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(d...

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  4. If y=sqrt(logx+sqrt(logx+sqrtlogx+......oo)), " then " dy/dx is

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  5. If x= e^(y+e^(y+....infty )),xgt 0,then (dy)/(dx)=

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  6. If y =e^(x+e^(x+e^(x+...infty ))),then (dy)/(dx) =

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

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  8. If y= (sin x )/( 1+(cos x )/(( sin x)/(1+ ....infty ))),then (dy)/(dx...

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  9. If x = 4t ,y =(4)/(t) ,then (dy)/(dx)=

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  10. If x=a(t-(1)/(t)),y=a(t+(1)/(t)), where t be the parameter, then (dy)/...

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  11. If x= at^(2) ,y= at ,then (dy)/(dx)=

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  12. If x = 2at^(2) ,y =at^(4) ,then (dy)/(dx) =

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  13. If x =a ((1-t^(2))/( 1+ t^(2))),y =(2bt )/(1+t^(2) ),then (dy)/(dx) =

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  14. If x=(2t)/(1+t^2),y=(1-t^2)/(1+t^2),t h e nfin d(dy)/(dx)a tt=2.

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  15. If x^(2) +y^(2) =t-(1)/(t) andx^(4) +y^(4) =t^(2) +(1)/( t^(2)),then (...

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  16. if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2 + 1/t^2 then prove that dy/dx...

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  17. If x=a cos theta ,y=asin theta ,then (dy)/(dx)=

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  18. If xsin t,y =cos 2t ,then (dy)/(dx) =

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  19. If x =a cot theta , y=b cosec theta ,then (dy)/(dx)=

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  20. If x = a sec theta, y = b tan theta " then " (dy)/(dx) = ?

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