1) y' = (4/5·x²)' - (2/x²)' + (3/∛x)' + (5^x)' =
= 4/5·2x - 2·[x^(-2)]' + 3·[x^(-1/3)]' + ln5 ·5^x =
= 1,6x - 2·(-2)·(x^(-2-1) + 3·(-1/3)·x^(-1/3-1) + ln5 · 5^x =
= 1,6x +4/x³ - 1/∛4 + ln5 · 5^x
2) y' = (lnx)'·(2/x +x) + lnx ·(2/x +x)' = 1/x ·(2/x +x) +lnx ·(-2/x² +1) =
= 2/x² + 1 + lnx - 2/x² ·lnx = 1+lnx +(1- lnx)·2/x² =
= 1 + lnx + ln(e/x) · 2/x²
3) y' = [(tgx)'·(x²+4) - tgx ·(x²+4)'] / (x²+4)² =
= [(x²+4)/cos²x - 2x·tgx] / (x²+4)²
4) y' = ln'((cos3x) · (cos3x)' =1/cos3x · ( -3sin3x) = - 3·tg3x