Home
Class 12
MATHS
If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then...

If `y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)),` then find `(dy)/(dx)a tx=0.`

A

0

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`y=((1-x)(1+x)(1+x^(2))(1+x^(4))…….(1+x^(2n)))/((1-x))`
`=(1-x^(4n))/(1-x)`
`rArr (dy)/(dx)=((1-x)(-4nx^(4n-1))-(1-x^(4n))(-1))/((1-x)^(2))`
`=(-4n(1-x)x^(4n-1)+(1-x^(4n)))/((1-x)^(2))`
`therefore ((dy)/(dx))_(x=0)=1`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 15

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

  • PRACTICE SET 17

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

If y=(1+x)(1+x^(2))(1+x^(4))...(1+x^(2n)) then find (dy)/(dx) at x=0

If y=(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^(n))) then (dy)/(dx) at x=0 is

If y=(1+x)(1+x^(2))(1+x^(4))(1+x^(8)) then (dy)/(dx) is:

If f'(x)=sqrt(2x^(2)-1) and y=f(x^(2)), then find (dy)/(dx) at x=1

If y=(x+(1)/(x))^(x)+(x^(2)+1)/(x^(2)-1), find (dy)/(dx)

If y=[(x^(2)+1)/(x+1)] , then find (dy)/(dx) .

y=x^(x cos x)+(x^(2)+1)/(x^(2)-1), find (dy)/(dx)

If y=f((2x-1)/(x^(2)+1)) and f'(x)=sin x^(2), find (dy)/(dx)

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 16-Paper - 2 (MATHEMATICS )
  1. The value of int(x^(2)+1)/(x^(2)-1)dx is

    Text Solution

    |

  2. If a=2sqrt(2),b=6,A=45^(@), then

    Text Solution

    |

  3. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

    Text Solution

    |

  4. int (dx)/(sin(x-a)sin(x-b)) is

    Text Solution

    |

  5. In DeltaABC 2a^2+4b^2+c^2=2ab+2ac then numerical value of cosB is

    Text Solution

    |

  6. The solution of the differential equation (e^(-2 sqrt(x))-(y)/(sqrt(x...

    Text Solution

    |

  7. Let f:(0,oo)to R and F(x)=int(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x...

    Text Solution

    |

  8. lim(nto oo)1/n+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n...

    Text Solution

    |

  9. The area bounded by y = sin^(-1)x,x=(1)/(sqrt(2)) and X-axis is

    Text Solution

    |

  10. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

    Text Solution

    |

  11. If the slope of one of the lines given by ax^(2)+2hxy+by^(2)=0 is 5 ti...

    Text Solution

    |

  12. The derivative of f(x)=3|2+x| at the point x0=-3 is

    Text Solution

    |

  13. The curve given by x + y = e^(xy) has a tangent parallel to the y-axis...

    Text Solution

    |

  14. Switching function of the network is

    Text Solution

    |

  15. Let p be the proposition that Mathematics is interesting and q be the ...

    Text Solution

    |

  16. The equation to a pair of opposite sides of a parallelogram are x^2-5x...

    Text Solution

    |

  17. In the adjoining circuit, the output s is

    Text Solution

    |

  18. The slope of tangent at (x,y) to a curve passing through (2, 1) is (x...

    Text Solution

    |

  19. The value of the integral int3^6 sqrtx/(sqrt(9-x)+sqrtx)dx is

    Text Solution

    |

  20. Find the probability that a leap year will have 53 Friday or 53 Sat...

    Text Solution

    |