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

If `y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s` `x/(2y-1)` (b) `x/(2y+1)` `1/(x(2y-1))` (d) `1/(x(1-2y))`

A

`x/(2y-1)`

B

`x/(2y+1)`

C

`1/(2y-x)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise DERIVATIVE OF PARAMETRIC FUNCTIONS|18 Videos
  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos
  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise DERIVATIVE OF INVERSE FUNCTIONS|27 Videos
  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos
  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

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

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

"If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))", show that "(2y-1).(dy)/(dx)=(1)/(x).

If y=sqrt(x+sqrt(x+sqrt(x+longrightarrow oo))), prove that (dy)/(dx)=(1)/(2y-1)

If =sqrt(log x+sqrt(log x+sqrt(log x+)rarr oo)) prove that (2y-1)(dy)/(dx)=(1)/(x)

If y=sqrt(x+sqrt(x+sqrt(x+...to oo)),) prove that (dy)/(dx)=(1)/(2y-1)

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

If y=sqrt(log x+sqrt(cos x+sqrt(cos x+...to oo))) prove that (dy)/(dx)=(sin x)/(1-2y)

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)

TARGET PUBLICATION-DIFFERENTIATION -LOGARITHMIC DIFFERENTIATION
  1. If cos(x+y) = y sinx, then (dy)/(dx)

    Text Solution

    |

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

    Text Solution

    |

  3. If sin(x+y)=log(x+y) then (dy)/(dx)=

    Text Solution

    |

  4. If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= -y/x (b) (3sin(x y)+4c...

    Text Solution

    |

  5. If x=ysqrt(1-y^(2)), then (dy)/(dx)=

    Text Solution

    |

  6. If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/...

    Text Solution

    |

  7. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

    Text Solution

    |

  8. If y=sqrt(sinx+y) , then (dy)/(dx) equals (cosx)/(2y-1) (b) (cosx)/(1-...

    Text Solution

    |

  9. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+......oo, then prove that (dy)/(dx)...

    Text Solution

    |

  10. If y=e^(x+e^(x+e^(x+..."to"oo)))," then: "(dy)/(dx)=

    Text Solution

    |

  11. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx) is equal to

    Text Solution

    |

  12. If y = x^(x ^(x^(x ^(x.... oo) then prove that x dy/dx = y^2/(1- y lo...

    Text Solution

    |

  13. The derivative of a^(sec x ) " w.r.t."a^(tan x ) (a gt 0) is

    Text Solution

    |

  14. Differentiate x=e^(theta)(theta+(1)/(theta)),y = e^(-theta)(theta-( 1)...

    Text Solution

    |

  15. x=a(cos t + log tan t/2), y =a sin t

    Text Solution

    |

  16. If x= a sin 2theta (1+ cos 2theta), y= b cos 2theta(1- cos 2theta), th...

    Text Solution

    |

  17. If x=t log t ,y =t^(t) ,then (dy)/(dx)=

    Text Solution

    |

  18. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

    Text Solution

    |

  19. The derivative of sin^(-1)((2x)/(1+x^2)) w.r.t. cos^(-1)((1-x^2)/(1+x^...

    Text Solution

    |

  20. The derivative of cos^(-1)((1-x^2)/(1+x^2)) w.r.t. cot^(-1)((1-3x^2)/(...

    Text Solution

    |