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)/(x(2y-1)`

D

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

Text Solution

Verified by Experts

`y=sqrt(log x+y)`
`"or "y^(2)=log x+y`
`"or "2y(dy)/(dx)=(1)/(x)+(dy)/(dx)or (dy)/(dx)=(1)/(x(2y-1))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 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(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

Solve (dy)/(dx)=sqrt(4x+2y-1)

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(sinx+sqrt(sinx+sqrt(sinx+...... tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)

If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+oo)))),t h e np rov et h a t(dy)/(dx)=(y^2-x)/(2y^3-2x y-1)

If sqrt(x) + sqrt(y)=4,then (dx)/(dy)at y=1.

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

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

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the val...

    Text Solution

    |

  2. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a)...

    Text Solution

    |

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

    Text Solution

    |

  4. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= 1/(2(1+x)sqrt(x)) (b) 3/((1+...

    Text Solution

    |

  5. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  6. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

    Text Solution

    |

  7. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  8. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

    Text Solution

    |

  9. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  10. If y=(x^x) then (dy)/(dx) is

    Text Solution

    |

  11. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

    Text Solution

    |

  12. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

    Text Solution

    |

  13. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  14. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  15. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x...

    Text Solution

    |

  16. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

    Text Solution

    |

  17. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

    Text Solution

    |

  18. The nth derivative of the function f(x)=1/(1-x^2) [where x in(-1,1) a...

    Text Solution

    |

  19. If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a)(x(dy)/(dx)-y)^2 (b)...

    Text Solution

    |

  20. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |