Найти производную функции y=1/2ln(x^2+2*x+2)+arctg(x+1)

Question

Найти производную функции
y=1/2ln(x^2+2*x+2)+arctg(x+1)

Answer 1

Y'=1/2·(ln(x²+2x+2))'+(arctg(x+1))'=1/2·(1/(x²+2x+2))·(x²+2x+2)'+(1/(1+(x+1)²))(x+1)'=
1/2·(1/x²+2x+2)·(2x+2)+(1/(1+x²+2x+1))·1=1/2·2(x+1)/(x²+2x+2+1/(x²+2x+2)=
(x+1)/(x²+2x+2)+1/(x²+2x+2)=(x+1+1)/(x²+2x+2)=(x+2)/(x²+2x+2).