А) y=x^(2/3) * lnx
y`=(x^(2/3))`*lnx + x^(2/3)*(lnx)` = (2/3)*x^(-1/3)*lnx + x^(2/3)*(1/x) = ((2/3)*lnx)/(x^1/3)
б) y= lnx / tgx
y` = ((lnx)`* tgx - lnx * (tgx)`) / (tgx)^2 = ( 1/x * tgx - lnx * 1/(cosx)^2) / (tgx)^2
в) y = arcsin (e^(2x))
y` = arcsin (e^(2x))` = 1/((1-x^2)^(1/2)) * (e^(2x))` = 1/((1-x^2)^(1/2)) * (e^(2x)) * (2x)` =1/((1-x^2)^(1/2)) * (e^(2x)) * 2 = (2 * e^(2x)) / ((1-x^2)^(1/2))
г) y = (sin5x)^3
y` = ((sin5x)^3)` = sin(5x+(3п/2)) * 5