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Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/...

Let `y=sqrt(x+sqrt(x+sqrt(x+oo)))` , `(dy)/(dx)` is equal to `1/(2y-1)` (b) `x/(x+2y)` `1/(sqrt(1+4x)` (d) `y/(2x+y)`

A

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

B

`(x)/(x+2y)`

C

`(1)/(sqrt(1+4x))`

D

`(y)/(2x+y)`

Text Solution

Verified by Experts

`y^(2)=x+y or (dy)/(dx)=(1)/(2y-1)`
`"Also, "y=(x)/(y)+1or (dy)/(dx)=(y)/(2x+y)`
`"Also, "y^(2)-y-x=0`
`"or "y=(1+sqrt(1+4x))/(2)" "("as " y gt0)`
`"or "y'=(1)/(4)(4)/(sqrt(1+4x))=(1)/(sqrt(1+4x))`
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CENGAGE-DIFFERENTIATION-Exercise (Multiple)
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  6. If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)...

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  8. If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0...

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  9. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

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  10. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

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  13. If a function is represented parametrically be the equations x=(1+(lo...

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  14. If y=(x^2)/2+1/2xsqrt(x^2+1)+(log)esqrt(x+sqrt(x^2+1)) , prove that 2y...

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  16. "If "e^(sin(x^(2)+y^(3)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can ...

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  17. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx)i se q u a lto (e^(sqrt...

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  18. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to 1/(2y-1) (b) ...

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  19. If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0...

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  20. If a function is represented parametrically be the equations x=(1+(lo...

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