Question

Вычислить производную функции

Answer 1

(u/v)'=(u'v-uv')/v²; здесь u=1+x*arctgx;  v=√(1+x²);

(xy)'=x'y+xy'

(const)'=0;

(√u)'=(1/(2√u))*u'

x'=1;

(arctgx)'=1/(1+x²);

y'=((arctgx+(x/(1+x²)))*(√(1+x²))-(1+x*arctgx)*(2x/(2√(1+x²)))/(1+x²)=

((arctgx+(x/(1+x²)))*(√(1+x²))-(1+x*arctgx)*(x/(√(1+x²)))/(1+x²)