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If y= sqrt (x+ sqrt (x+ sqrt (x))),then...

If ` y= sqrt (x+ sqrt (x+ sqrt (x))),then (dy)/(dx) =`

A

` (1)/(sqrt(x+sqrtx+ sqrtx) )(1+ (1)/(sqrt( x+sqrt(x) ))( 1+(1)/(sqrt(x))))`

B

` (1)/(2sqrt(x+sqrtx+ sqrtx) )(1+ (1)/(sqrt( x+sqrt(x) ))( 1+(1)/(sqrt(x))))`

C

` (1)/(2sqrt(x+sqrtx+ sqrtx) )(1+ (1)/(2sqrt( x+sqrt(x) ))( 1+(1)/(sqrt(x))))`

D

` (1)/(2sqrt(x+sqrtx+ sqrtx) )(1+ (1)/(2sqrt( x+sqrt(x) ))( 1+(1)/(2sqrt(x))))`

Text Solution

Verified by Experts

The correct Answer is:
D
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