Seeking help with finishing this problem, from line 6 from bottom (with ???).

Find dy/dx and d^2y/dx^2 for,

y = ln sin^4 t and x = ln cos^8 t

y = ln sin^4 t

dy/dt = 1/sin^4 t X (cos^4 t)

= cos^4 t/sin^4 t

= cot^4 t

x = ln cos^8 t

dx/dt = 1/cos^8 t X (-sin^8 t)

= -sin^8 t/cos^8 t

= -tan^8 t

dy/dx = dy/dt X dt/dx

= cot^4 t X -1/tan^8 t

= cot^4 t X (-cot^8 t)

= -(cot^4 t X cot^8 t)

d^2y/dx^2 = d(dy/dx)/dx

= d(-cot^4 t X cot^8 t)/dx

dy/dt = -[-cot^4 t.(cosec^2)^8 t] + [cot^8 t.cosec^2)^4 t]

= [cot^4 t.cosec^16 t] + [cot^8 t.cosec^8 t]

= cot^4 t.cosec^8 t(cosec^2 t + cot^2 t) ???

d^2y/dx^2 = dy/dt X dt/dx

= [cot^4 t.cosec^8 t(cosec^2 t + cot^2 t)] X -1/tan^8 t

= [cot^4 t.cosec^8 t(cosec^2 t + cot^2 t)] X -cot^8 t

Thanks for your help.