[y=tan^(-1)(1)/(x^(2)+x+1)+tan^(-1)(1)/(x^(2)+3x+3)+tan^(-1)(1)/(x^(2)+5x+7)+..." nterms "],[" then "(dy)/(dx)=]

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

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

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))+ 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 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