Home
Class 12
MATHS
Let y=(x^(8)+x^(4)+1)/(x^(4)+x^(2)+1)."I...

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

A

`a = 4 , b = 2`

B

` a = 4, b = - 2 `

C

` a = - 2, b = 4 `

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(d)/(dx) [((1 + x^(2) + x^(4))(1 - x^(2) +x^(4)))/((1 +x^(2) + x^(4)))] = ax^(3) + dx `
` rArr (d)/(dx) (1 - x^(2) + x^(4)) = ax^(3) + bx `
`rArr - 2x + 4x^(3)= ax^(3) + bx `
` rArr a = 4 " and " b = - 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=(x^(4)+x^(2)+1)/(x^(2)+x+1) find (dy)/(dx) =

If y=(x^(4)+x^(2)+1)/(x^(2)+x+1) and (dy)/(dx)= ax^(2)+bx+c then the value of a+b+c is

If y=(x^(4)+x^(2)+1)/(x^(2)+x+1) and (dy)/(dx)=ax^(2)+bx+c then the value of a+b+c is

If y=(x^(4)+x^(2)+1)/(x^(2)+x+1) and (dy)/(dx)=ax^(2)+bx+c then the value of a+b+c is

If : y=cos^(-1)(8x^(4)-8x^(2)+1)," then: "(dy)/(dx)=

(x-x^(3))(dy)/(dx)+(2x^(2)-1)y=ax^(3)

quad y=x^(5)+x^(4)+x^(3)+x^(2)+x+1. Find ((dy)/(dx))

if y=(x^(4)-x^(2)+1)/(x^(2)+sqrt(3)x+1) and (dy)/(dx)=ax+b then the value of a+b is equal to

If y=(x^(4)+x^(2)+1)/(x^(2)+x+1) then (dy)/(dx)=ax+b, find a and b

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

    Text Solution

    |

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

    Text Solution

    |

  6. if y=sin^-1[sqrt(x-ax)-sqrt(a-ax)] then prove that 1/(2sqrtx sqrt(1-x)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  16. If f(x) = (x - 1)/(4) + ((x - 1)^(2))/(12) + ((x -1)^(5))/(20) + ((x -...

    Text Solution

    |

  17. If x=e^tsint,y=e^tcost then (d^2y)/(dx^2) at x=pi is

    Text Solution

    |

  18. (d^2x)/(d y^2) equals

    Text Solution

    |

  19. If x=sint and y=cos pt, then

    Text Solution

    |

  20. If a=A cos 4t+B sin4t, then (d^(2)x)/(dt^(2)) is equal to

    Text Solution

    |