Home
Class 12
MATHS
If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . ...

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

A

sin x

B

` - cos x `

C

cos x

D

` - sin x `

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `y = sqrt( sinx + sqrt(sin x + sqrt(sin x + ...oo))) `
` therefore y = sqrt(sin x + y)rArr y^(2) = sin x + y`
On differentiating both sides w.r.t.x, we get
`2y (dy)/(dx) = cos x + (dy)/(dx) `
` rArr (2y -1) (dy)/(dx) = cos x `
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|80 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

Similar Questions

Explore conceptually related problems

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx..." to "oo)))," then "(2y-1)y_(1)=

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

If y = sqrt(sinx+y) , then (dy)/(dx) is equal to

If y=2 +sqrt(sinx+2+sqrt(sinx+2+sqrt(sinx+…oo))) then the value of (dy)/(dx) at x = 0 is

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

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

If y=log_(cosx)sinx, then (dy)/(dx) is equal to

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , where 0lt xlt(pi)/(2), then (dy)/(dx) is equal to

If y=(sinx)^(sinx)^(((sinx)dotoo)) , then (dy)/(dx) is equal to.........

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
  1. Find (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta and y = 2sin...

    Text Solution

    |

  2. find the derivative of e^(x) + e^(y) = e^(x +y)

    Text Solution

    |

  3. If xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) is equal to

    Text Solution

    |

  4. The derivative of cos^(3)x w.r.t. sin^(3)x is

    Text Solution

    |

  5. The derivative of log|x| is

    Text Solution

    |

  6. The function f(x)=e^(-|x|) is

    Text Solution

    |

  7. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

    Text Solution

    |

  8. If y = log(cos x) sin x " then" (dy)/(dx) is equal to

    Text Solution

    |

  9. If y^(2) = ax^(2) + bx + c , where a,b,c, are constants , then y^...

    Text Solution

    |

  10. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  11. If y = 5^(x) x^(5) , " then" (dy)/(dx) is

    Text Solution

    |

  12. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

    Text Solution

    |

  13. (d)/(dx)[sec{cos^(-1) ((x)/(8))}] is equal to

    Text Solution

    |

  14. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

    Text Solution

    |

  15. If y = a sin^(3) theta " and " x = a cos^(3) theta . " then at " th...

    Text Solution

    |

  16. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . .oo))), then (dy)/(dx) is equa...

    Text Solution

    |

  17. The nth derivatiive of (x+1)^n is

    Text Solution

    |

  18. If y = a sin (5x + c) , then

    Text Solution

    |

  19. If sin (xy) + (x)/(y) =x^(2) - y , " then " (dy)/(dx) is equal to

    Text Solution

    |

  20. If y=x^(tanx)+sqrt((x^2+1)/2),fin d(dy)/(dx)

    Text Solution

    |