Verified answer

((5+tg^3x)^3)'=3* (5+tg^3x)^(3-1) * (5+tg^3x)'=3* (5+tg^3x)^2 * ((5)'+(tg^3 x)')=

=3* (5+tg^3x)^2 *(0+3*tg^(3-1) x *(tg x)')=3* (5+tg^3x)^3 * tg^2 x/cos^2 x

y'=3(5+tg^3x)^2 * (0+1/cos^6x)