Home
Class 12
MATHS
If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo)))...

If `y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo)))` then `(dy)/(dx)` equal to

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))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Matrix Match Type|6 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Execrises|137 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let y=sqrt(x+sqrt(x+sqrt(x+...oo))) , then (dy)/(dx) is equals to -

If y = sqrt(x+sqrt(x+sqrt(x+* * * infty))) then (dy)/(dx)=

"If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(dx)=(y^(2)-x)/(2y^(3)-2xy-1)

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to -

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

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)) ,then (dy)/(dx) is equal to (a) (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (c) (a y)/(xsqrt(a^2-x^2)) (d) none of these

If y=e^(sqrt(x))-e^(-sqrt(x))," then "(dy)/(dx) is equal to

If y=sqrt(sinx+sqrt(sinx+sqrt(sin+...oo))) , find dy/dx

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2sqrtx) (c) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

If y=sqrt(sin x+sqrt(sinx+sqrt(sinx+…..oo))) show that (dy)/(dx) =(cos x )/(2y-1)

CENGAGE PUBLICATION-DIFFERENTIATION-Multiple Correct Answers Type
  1. f(n)(x)=e^(f(n-1)(x))" for all "n in N and f(0)(x)=x," then "(d)/(dx){...

    Text Solution

    |

  2. Let f(x)a n dg(x) be two function having finite nonzero third-order de...

    Text Solution

    |

  3. If y=e^(-x)cosxa n dyn+kn y=0,w h e r eyn=(d^(n y))/(dx^n)a n dkn are ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

    Text Solution

    |

  7. If y=(sinx)^x,then dy/dx=

    Text Solution

    |

  8. If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i ...

    Text Solution

    |

  9. If for x (0,1/4), the derivative of tan^(-1)((6xsqrt(x))/(1-9x^3)) is ...

    Text Solution

    |

  10. Let f(x)=xsinpix ,\ x >0 . Then for all natural numbers n ,\ f^(pr...

    Text Solution

    |

  11. Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x ...

    Text Solution

    |

  12. Let f:R to R and h:R to R be differentiable functions such that f(x)=x...

    Text Solution

    |

  13. If y=e^(sqrt(x))-e^(-sqrt(x))," then "(dy)/(dx) is equal to

    Text Solution

    |

  14. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

    Text Solution

    |

  15. If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

    Text Solution

    |

  19. Let f(x)=xsinpix ,\ x >0 . Then for all natural numbers n ,\ f^(pr...

    Text Solution

    |

  20. Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x ...

    Text Solution

    |