Question # 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}+ldots+ ) upto ( n ) terms, then ( y^{prime} ) ( '(0) ) is equal to

# 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}+ldots+ ) upto ( n ) terms, then ( y^{prime} ) ( '(0) ) is equal to

(a) ( -1 /left(n^{2}+1right) )

(b) ( -n^{2} /left(n^{2}+1right) )

(c) ( n^{2} /left(n^{2}+1right) )

(d) none of these

Solution

Ans.

(b)

(@) Solution: ( y=tan ^{-1} frac{1}{1+x+x^{2}}+tan ^{-1} frac{1}{x^{2}+3 x+3}+ )