Home
Class 12
MATHS
If f(x)=sin^(-1)(sinx)+cos^(-1)(sinx) an...

If `f(x)=sin^(-1)(sinx)+cos^(-1)(sinx) and phi(x)=f(f(f(x)))`, then `phi'(x)` is equal to

A

1

B

`sin x `

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) = pi //2 ` (a constant function)
`[because sin^(-1) x + cos^(-1) x = (pi)/(2)]`
` therefore phi (x) = f(f((pi)/(2))) = (pi)/(2) rArr phi' (x) = 0 `
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORER|35 Videos

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 (HIGHER ORDER DERIVATIVE )|15 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

The function f(x)=sin^(-1)(sinx) , is

int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx=(f(x))/((sinx)^(7))+C , then f(x) is equal to

If inte^(x)((1-sinx)/(1-cosx))dx=f(x)+ Constant, then f(x) is equal to

int({f(x)phi'(x)-f'(x)phi(x)})/(f(x)phi(x)){ ln phi(x)-lnf(x)}dx is equal to

Let f(x)=sinx,g(x)=2x" and "h(x)=cosx. If phi(x)=["go"(fh)](x)," then "phi''((pi)/(4)) is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If x^(y) = e^(2(x-y)), " then" f'(x) is equal to

    Text Solution

    |

  2. If sqrt(1-x^(2n))+sqrt(1-y^(2n))=a^n(x^n-y^n), prove that y^(n-1)*sqr...

    Text Solution

    |

  3. If f(x)=sin^(-1)(sinx)+cos^(-1)(sinx) and phi(x)=f(f(f(x))), then phi'...

    Text Solution

    |

  4. Let x^cosy + y^cosx = 5, then

    Text Solution

    |

  5. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

    Text Solution

    |

  6. If y=tan^(-1)1/(1+x+x^2)+tan^(-1)1/(x^2+3x+3)+tan^(-1)1/(x^2+5x+7)++ u...

    Text Solution

    |

  7. If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to

    Text Solution

    |

  8. If y = cos^(-1) ((2cos x - 3 sin x)/(sqrt(13))), " then" (dy)/(dx) i...

    Text Solution

    |

  9. Let y=(x^(8)+x^(4)+1)/(x^(4)+x^(2)+1)."If"(dy)/(dx)=ax^(3)+bx. Then,

    Text Solution

    |

  10. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (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=sin^-1[sqrt(x-ax)-sqrt(a-ax)] then prove that 1/(2sqrtx sqrt(1-x)...

    Text Solution

    |

  13. If y=log(x^(2)+4)(7x^(2)-5x+1), then (dy)/(dx) is equal to

    Text Solution

    |

  14. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

    Text Solution

    |

  15. If x^(2) + y^(2) = a^(2) , then a is equal to

    Text Solution

    |

  16. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) i...

    Text Solution

    |

  17. If y = sin^(n) x cos nx, " then" (dy)/(dx) is

    Text Solution

    |

  18. If y = sec^(-1) [ "cosec x"] + "cosec"^(-1) [sec x] + sin^(-1) [cos x...

    Text Solution

    |

  19. If f(x)=(g(x)+g(-x))/2 + 2/[h(x)+h(-x)]^(-1), where g and h are diffe...

    Text Solution

    |

  20. If y = e^(x) * e^(x^(2)) *e^(x^(3) )*...*e^(x^(n))..., " for " - lt x ...

    Text Solution

    |