Question

(arctgx)^x производная

Answer 1

$y=(arctgx)^x\\lny=ln(arctgx)^x\\lny=x*ln(arctgx)\\(lny)'=x'*ln(arctgx)+x*(ln(arctgx))'\\\frac{1}y*y'=ln(arctgx)+\frac{x}{arctgx}*(arctgx)'\\\\\frac{1}y*y'=ln(arctgx)+\frac{x}{arctgx}*\frac{1}{1+x^2}\\\\y'=(arctgx)^x(ln(arctgx)+\frac{x}{(x^2+1)(arctgx)})$