Home
Class 12
MATHS
If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2...

If `y=sum_(r=1)^(x) tan^(-1)((1)/(1+r+r^(2)))`, then `(dy)/(dx)` is equal to

A

`(1)/(1+x^(2))`

B

`(1)/(1+(1+x)^(2))`

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

sum_(i=1)^(oo)tan^(-1)((1)/(2r^(2)))=

sum_(r=1)^9 tan^-1(1/(2r^2)) =

sum_(r=1)^(oo)tan^(-1)((2)/(1+(2r+1)(2r-1)))

lim_(x to oo ) tan { sum_(r=1)^(n) tan^(-1) ((1)/( 1 +r +r^2))} is equal to ________.

The value of the lim_(n rarr oo)tan{sum_(r=1)^(n)tan^(-1)((1)/(2r^(2)))}_( is equal to )

If sum_(r=1)^(oo) cot^(-1)(((r+1)^(2))/(2))=tan^(-1)x then x is equal to

ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))), where -pi/4 lt ...

    Text Solution

    |

  2. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(1)/(4) is equal to

    Text Solution

    |

  3. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

    Text Solution

    |

  4. If y=(sin^(-1)(sinalphasinx)/(1-cosalphasinx)), then y'(0) is equal to

    Text Solution

    |

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

    Text Solution

    |

  6. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  7. If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...

    Text Solution

    |

  8. If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )(...

    Text Solution

    |

  9. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

    Text Solution

    |

  10. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

    Text Solution

    |

  11. Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...

    Text Solution

    |

  12. if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...

    Text Solution

    |

  13. If f(x)=-(x^(3))/(3)+x^(2)sina.sin2a-5sin^(-1)(a^(2)-8a+17),then

    Text Solution

    |

  14. Let f and g be differentiable functions satisfying g(a) = b,g' (a) = ...

    Text Solution

    |

  15. The derivative of the function, f(x)=cos^(-1){(1)/(sqrt13)(2cosx-3sin...

    Text Solution

    |

  16. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

    Text Solution

    |

  17. Let y=ln(1+cosx)^(2), then the value of(d^(2)y)/(dx^(2))+(2)/(e^(y//2)...

    Text Solution

    |

  18. If f(x)=(a+sqrt(a^2-x^2)+x)/(sqrt(a^2-x^2)+a-x) where a>0 and x<a then...

    Text Solution

    |

  19. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x)...

    Text Solution

    |

  20. If f(x)=|log(e)|x||," then "f'(x) equals

    Text Solution

    |