Question

Найти производные функции  (1/x)^arctg3x

Answer 1

( (1/x)^arctg(3x) )' = ( (x)^(-arctg3x) )' = -arctg(3x)*x^(-arctg3x - 1) * 3/(1 + 9x^2) = -3*arctg(3x) / ((1+9x^2)*(x^arctg3x + 1))