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

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

Text Solution

Verified by Experts

The correct Answer is:
1
`(dy)/(dx)=1(1+x^(2))(1+x^(4))...(1+x^(2^(n)))+2x(1+x)(1+x^(4))...(1+x^(2^(n)))`
`+4x^(3)(1+x)(1+x^(2))(1+x^(8))...(1+x^(2^(n)))`
:
`+2^(n)x^(2^(n-1))(1+x)(1+x^(2))...(1+x^(2^(n-1)))`
`"or "(dy)/(dx):|_(x=0)=1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.3|8 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.4|10 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.1|7 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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

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

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

If y=tan^(-1)((2x)/(1-x^2))" find "(dy)/(dx) .

For x^(2)+y^(2)=1 find dy/dx

For x^(2)+y^(2)=1 find dy/dx

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

CENGAGE-DIFFERENTIATION-Exercise 3.2
  1. If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(pri...

    Text Solution

    |

  2. sin^(-1) ((2x)/(1 + x^(2)))

    Text Solution

    |

  3. Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))...

    Text Solution

    |

  4. Find (dy)/(dx) in the following : y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt...

    Text Solution

    |

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

    Text Solution

    |

  6. "F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

    Text Solution

    |

  7. y=tan^(-1)(x/(1+sqrt(1-x^2)))

    Text Solution

    |

  8. Find (dy)/(dx) for the function: y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)

    Text Solution

    |

  9. Find (dy)/(dx) for the function: y=sqrt(sinsqrt(x))

    Text Solution

    |

  10. Differentiate : y = e^(sin 2x)

    Text Solution

    |

  11. Find (dy)/(dx) for the function: y=logsqrt(sinsqrt(e^x))

    Text Solution

    |

  12. Find (dy)/(dx) for the function: y=a^((sin^(-1)x))^2

    Text Solution

    |

  13. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

    Text Solution

    |

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

    Text Solution

    |

  15. Find (dy)/(dx) for the functions: y=x^3e^xsinx

    Text Solution

    |

  16. Find (dy)/(dx) for the function: y=(log)esqrt((1+sinx)/(1-sinx)),w h e...

    Text Solution

    |

  17. y=(x+sin x)/(x+cos x)

    Text Solution

    |

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

    Text Solution

    |

  19. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((1+x)^2)

    Text Solution

    |

  20. If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(pri...

    Text Solution

    |