Put u = x − cos2x and then y = u4.

Now

`(du)/(dx)=1-2\ cos x(-sin x)`

`=1+2\ sin x\ cos x`

and

`(dy)/(du)=4u^3`

So we have:

`(dy)/(dx)=(dy)/(du)(du)/(dx)`

`=4u^3(du)/(dx)`

`=4[x-cos^2x]^3[1+` `{:2 sin x cos x]`