Home
Class 12
MATHS
If y=(a^cos^((-1)x))/(1+a^cos^((-1)x)) a...

If `y=(a^cos^((-1)x))/(1+a^cos^((-1)x))` and `z=a^cos^((-1)x)` , then `(dy)/(dz)` is equal to........

A

`(1)/(1 + a^(cos^(-1) x))`

B

`-(1)/(1 + a^(cos^(-1) x))`

C

`(1)/((1 + a^(cos^(-1) x))^(2))`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
`y= (a^(cos^(-1)))/(1 + a ^(cos^(-1)x)), z = a^(cos^(-1))rArr = (z)/(1 + z)`
` rArr (dy)/(dx) = ((1 + z)1 - z(1))/((1 + z)^(2)) = (1)/((1 + z)^(2))`
`= (1)/(( 1 + x^(cos^(-1)x))^(2))`
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

If y=(a^(cos^-1x))/(1+a^(cos^-1x))andz=a^(cos^-1x),then (dy)/(dx) =

If y=cos^(-1) (cos x),"then " (dy)/(dx) is

If y=(sin^(-1)x-cos^(-1)x)/(sin^(-1)x+cos^(-1)x)," then "(dy)/(dx)=

If y = cos^(-1) x^(3) " then " (dy)/(dx)= ?

If y=sin^(-1)x,z=cos^(-1)sqrt(1-x^(2))," then: "(dy)/(dz)=

If y=cos((1)/(2)cos^(-1)x)," then "(dy)/(dx)=

If y=sin^(-1)x+cos^(-1)x, find (dy)/(dx)

If sin^(2) x + cos^(2) y = 1 , " then " (dy)/(dx) is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If x = tan""(y)/(2) - log[((1 + tan""(y)/(2))^(2))/(tan""(y)/(2))], "t...

    Text Solution

    |

  2. If y=sec^-1([sqrtx+1]/[sqrtx-1])+sin^-1([sqrtx-1]/[sqrtx+1]), then dy/...

    Text Solution

    |

  3. If y=(a^cos^((-1)x))/(1+a^cos^((-1)x)) and z=a^cos^((-1)x) , then (dy)...

    Text Solution

    |

  4. If y= log x . e ^((tan x + x ^(2))), " then" dy/(dx) is equal to

    Text Solution

    |

  5. if y=log(sinx) tanx then ((dy)/(dx)) (pi/4) is

    Text Solution

    |

  6. If y = ((ax + b)/(cx + d)), "then" 2 (dy)/(dx).(d^(3) y)/(dx^(3)) is...

    Text Solution

    |

  7. If 5f(x)+3f(1/x)=x+2 and y=x f(x), then find dy/dx at x=1.

    Text Solution

    |

  8. If y is a function of x and log(x+y)-2xy=0 then the value of y (0) is ...

    Text Solution

    |

  9. If y = f(x^(2) + 2) " and " f'(3) = 5 , " then" dy/dx " at x " = 1 is

    Text Solution

    |

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

    Text Solution

    |

  11. let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) then find (h^(prime)(x...

    Text Solution

    |

  12. If y = (cos x)^((cosx)^((cos x)...oo)), " then " dy/dx is equal to

    Text Solution

    |

  13. If cos(x/2) cos (x/2^2) cos (x/2^) ..... cos (x/2^n)=sinx/(sin(x/2^n) ...

    Text Solution

    |

  14. If x = log (1 + t^(2)) " and " y = t - tan^(-1)t, " then" dy/dx is e...

    Text Solution

    |

  15. If the function y(x) reprsented by x = sin t , y = ae^(tsqrt(2)) + be...

    Text Solution

    |

  16. If y=sqrt((a-x)(x-b))-(a-b)tan^(-1)(sqrt(a-x)/sqrt(x-b)) then dy/dx=

    Text Solution

    |

  17. If x=sectheta-costheta,y=sec^(10)theta-cos^(10)theta and (x^(2)+4)((dy...

    Text Solution

    |

  18. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

    Text Solution

    |

  19. If x^(y) = e^(2(x-y)), " then" f'(x) is equal to

    Text Solution

    |

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

    Text Solution

    |