Question

Помогите первая производная y= arctg^7 (x^2+1)

Answer 1

производная сложной функции
f'(g(x))=f'(g)*g'(x)
y'=7arctg^6(x²+1)*(arctg(x²+1))'=7(arctg^6(x²+1))[1/(1+(x²+1)²)](x²+1)'=
=7(arctg^6(x²+1))2x/(1+(1+x²)²)=14x(arctg^6(x²+1)/(2+2x²+x^4)