d/dx(sec^3 x tan^3x)=
d/dx(secx) = secx*tanx and d/dx(tanx) = sec^2x
product rule
d/dx(sec^3x )*tan^3x + sec^3x*d/dx(tan^3x)=
chain rule
3sec^2x*d/dx(secx)*tan^3x + sec^3x*3tan^2x*d/dx(tanx)=
3sec^2x*secx*tanx*tan^3x + sec^3x*3tan^2x*sec^2x=
3sec^4x*tan^4x + 3sec^5x*tan^2x=
3sec^4x*tan^2x(tan^2x+secx)