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

`y= tan^(-1) "" (1)/(1+x+x^2) + tan^(-1) "" (1)/(x^2 +3x+3) + tan^(-1) "" (1)/( x^2 +5x +7)+ `n terms then y'(0)=

A

`-(n^2)/(1+n^2)`

B

`pi/2`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

If y = tan^(-1) ((1)/(x^(2) + x + 1)) + tan^(-1) ((1)/( x^(2) + 3x + 3)) + tan^(-1) ((1)/( x^(2) + 5x + 7))+ tan^(-1) ((1)/( x^(2) +7x + 13)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

If =tan^(-1)(1)/(1+x+x^(2))+tan^(-1)(1)/(x^(2)+3x+3)+tan^(-1)(1)/(x^(2)+5x+7)+ upto n terms,then find the value of y'(0) .

If y=tan^(-1).(1)/(1+x+x^(2))+tan^(-1).(1)/(x^(2)+3x+3) upto +tan^(-1).(1)/(x^(2)+5x+7)+….+2n terms (AA x ge0), then y(0) is

If y=tan^(-1)((1)/(x^(2)+x+1))+tan^(-1)((1)/(x^(2)+3x+3))+tan^(-1)((1)/(x^(2)+5x+7))+ to nterms,show that (dy)/(dx)=(1)/((x+n)^(2)+1)-(1)/(x^(2)+1)

If y = tan ^ (- 1) ((1) / (1 + x + x ^ (2))) + tan ^ (- 1) ((1) / (x ^ (2) + 3x + 3)) + tan ^ (- 1) ((1) / (x ^ (2) + 5x + 7)) then y '(0) = (i) - (3) / (10) (ii) - (5) / (10) (iii) - (7) / (10) (iv) - (9) / (10)

tan ^ (- 1) ((1) / (x + y)) + tan ^ (- 1) ((y) / (x ^ (2) + xy + 1)) = cot ^ (- 1) x