If y=tan−111+x+x2+tan−11x2+3x+3 +tan−11x2+5x+7+tan−11x2+7x+13+...+ n terms then y'0 is equal to

$y = \tan^{- 1} \frac{1}{1 + x + x^{2}} + \tan^{- 1} \frac{1}{x^{2} + 3 x + 3} + ... +$ upto terms

$= \tan^{- 1} \frac{(x + 1) - x}{1 + x (x + 1)} + \tan^{- 1} \frac{(x + 2) - (x + 1)}{1 + (x + 1) (x + 2)} + ... n$ terms

$= \tan^{- 1} (x + 1) - \tan^{- 1} x + \tan^{- 1} (x + 2) - \tan^{- 1} (x + 1) + ... +$

$\tan^{- 1} (x + n) - \tan^{- 1} (x + (n - 1))$

$= \tan^{- 1} (x + n) - \tan^{- 1} x .$

$y^{'} (x) = \frac{1}{1 + {(x + n)}^{2}} - \frac{1}{1 + x^{2}}$

$\Rightarrow y^{'} (0) = \frac{1}{1 + n^{2}} - 1 = - \frac{n^{2}}{1 + n^{2}}$

If $y = \tan^{- 1} \frac{1}{1 + x + x^{2}} + \tan^{- 1} \frac{1}{x^{2} + 3 x + 3} + \tan^{- 1} \frac{1}{x^{2} + 5 x + 7} + \tan^{- 1} \frac{1}{x^{2} + 7 x + 13} + ... + n t e r m s$
then $y^{'} (0)$ is equal to