4. = (sinx)^x * (lnsinx + (x/sinx) * (sinx)' )) = (sinx)^x * (lnsinx + (x/sinx) * cosx * x' = (sinx)^x * (lnsinx + (x/sinx) * cosx) = ... правильно?

2. да, пропустила знак ' , спасибо
= [2x * arctgx * ln(x^2 + 1)] + [(x^2 + 1) * 1/(1+ x^2) * ln (x^2 + 1)] +

+ [(x^2 + 1) * arctgx * 1/(x^2 +1) * (x^2 +1)' ] = 2x * arctgx * ln(x^2 + 1) + ln (x^2 + 1) + 2xarctgx =

= 2xarctgx * (ln(x^2 + 1) +1) + ln (x^2 +1) =....