Home
Class 12
MATHS
If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(....

If `y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo)`, show that, `x (dy)/(dx)=(y^(2))/(2-y log x).`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3A ( Long Answer Type Questions)|50 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Multiple Choice Type Questions)|9 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3A (Very Short Answer Type Questions)|90 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If (sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo))) and x(dy)/(dx) =(f(y))/( 2-y log x) , then the value of f(y) is -

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

If y=e^(x^(e ^(x^(...oo)))) ,show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x logy)) .

If y=a^(x^(a^(x^(…oo)))) , show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x log y)) .

(dy)/(dx)=sqrt(y-x)

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

"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 = sqrt(x/(a))-sqrt(a/(x)) show that 2xy (dy)/(dx)=(x)/(a)-(a)/(x)

If x=y^(y^(y^(...oo))) , then show that, (dy)/(dx)=(y(1-x logy))/(x^(2)) .

If y sqrt(x^(2)+1)=log(sqrt(x^(2)+1)-x) , show that, (x^(2)+1)(dy)/(dx)+xy+1=0

CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(...

    Text Solution

    |

  2. Differentiate the following functions w.r.t. t : sqrt(t) e^(t) sec...

    Text Solution

    |

  3. Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)

    Text Solution

    |

  4. Differentiate the following functions w.r.t. t : (u sin u+cos u)/(u...

    Text Solution

    |

  5. If x=a(theta+sin theta) and y=a(1+cos theta), then find the simplified...

    Text Solution

    |

  6. If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)), show...

    Text Solution

    |

  7. Find the differential coefficient of : (tan^(-1)x)/(1+tan^(-1)x)" ...

    Text Solution

    |

  8. Find the differential coefficient of : "tan"^(-1)(sqrt(1+x^(2))-1)/...

    Text Solution

    |

  9. Find the differential coefficient of : "cos"^(-1)(1-x^(2))/(1+x^(2...

    Text Solution

    |

  10. Find the differential coefficient of : x^(sin^(-1)x)" w.r.t. " sin...

    Text Solution

    |

  11. If y=(x)/(sqrt(1+x^(2))), prove that, x^(3)(dy)/(dx)=y^(3).

    Text Solution

    |

  12. If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)).

    Text Solution

    |

  13. If ye^(y)=x, prove that, (dy)/(dx)=(y)/(x(1+y)).

    Text Solution

    |

  14. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), show that, (dy)/(dx)=(sqrt(1-...

    Text Solution

    |

  15. If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x), prove that the value of (dy...

    Text Solution

    |

  16. If y=sin((pi)/(6)e^(xy)), find (dy)/(dx) at x=0.

    Text Solution

    |

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

    Text Solution

    |

  18. If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo), show that, x (dy)/(dx)...

    Text Solution

    |

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

    Text Solution

    |

  20. Show that the derivative of (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2...

    Text Solution

    |