Home
Class 12
MATHS
If y=(sinx)^((sinx)^((sinx)^(...^infty)...

If `y=(sinx)^((sinx)^((sinx)^(...^infty)))` , prove that `(dy)/(dx)=(y^2cosx)/((1-ylogsinx)`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If y=sinx^(sinx^(sinx^dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-ylogsinx))

Prove that (1-sinx)/(cosx)=(cosx)/(1+sinx)

If (sinx)^y=x+y , prove that (dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsinx-1)

If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))) ,prove that (dy)/(dx)=(cosx)/(2y-1)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(dx)=(cosx)/(2y-1)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(dx)=(cosx)/(2y-1)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(dx)=(cosx)/(2y-1)

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

If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...tooo))), prove that (dy)/(dx)=(sinx)/(1-2y)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function sin^(-1)(x/(x^2+a^2))

    Text Solution

    |

  2. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...tooo))), prove that (dy)/(dx)=...

    Text Solution

    |

  3. If y=(sinx)^((sinx)^((sinx)^(...^infty))) , prove that (dy)/(dx)=(y^...

    Text Solution

    |

  4. Differentiate the following function from first principles: logcosx

    Text Solution

    |

  5. If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(...

    Text Solution

    |

  6. Find (dy)/(dx), y=e^(3x)sin4x. 2^x

    Text Solution

    |

  7. Differentiate the following function from first principles: e^(sqrt...

    Text Solution

    |

  8. Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sq...

    Text Solution

    |

  9. Differentiate the following functions with respect to (sin^(-1)x^4)...

    Text Solution

    |

  10. Find (dy)/(dx), y=((x^2-1)^3(2x-1))/(sqrt((x-3)(4x-1)))

    Text Solution

    |

  11. If sqrt(y+x)+sqrt(y-x)=c ,show that (dy)/(dx)=y/x-sqrt((y^2)/(x^2)...

    Text Solution

    |

  12. If (sinx)^y=(cosy)^x ,p rov et h a t(dy)/(dx)=(logcosy-ycotx)/(logsinx...

    Text Solution

    |

  13. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

    Text Solution

    |

  14. If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

    Text Solution

    |

  15. If xsin(a+y)+sina cos(a+y)=0, prove that (dy)/(dx)=sin^2(a+y)/sina

    Text Solution

    |

  16. Find (dy)/(dx) in each of the following: (x^2+y^2)^2=x y

    Text Solution

    |

  17. Differentiate the following functions (2^xcosx)/((x^2+3)^2) with res...

    Text Solution

    |

  18. Differentiate the following functions with respect to e^sin^((-1...

    Text Solution

    |

  19. Differentiate the function "sin"(2sin^(-1)x) with respect to x.

    Text Solution

    |

  20. Differentiate the following function sqrt(tan^(-1)(x/2)) with respec...

    Text Solution

    |