Putting `sqrtx=t, sin sqrtx=sin t=u and sqrt(sin sqrtx)=sqrtu=v`, we get
`y=sin v, v =sqrtu, u = sin t and t=sqrtx`.
`therefore" "(dy)/(dv)=cosv,(dv)/(du)=(1)/(2)u^(-1//2)=(1)/(2sqrtu)=cost and (dt)/(dx)=(1)/(2sqrtx)`
So, `(dy)/(dx)=((dy)/(dv)xx(dv)/(du)xx(du)/(dt)xx(dt)/(dx))=[cos v.(1)/(2sqrtu).cost.(1)/(2sqrtx)]`
`=[cossqrtu.(1)/(2sqrtu)cost.(1)/(2sqrtx)]" "[becausev=sqrtu]`
`=(1)/(4)cos(sqrtsint).(1)/(sqrtsint).cossqrtx.(1)/(sqrtx)" "[becauseu=sint]`
`=(1)/(4)cos(sqrt(sinsqrtx)).(1)/(sqrt(sinsqrtx)).cossqrtx.(1)/(sqrtx)" "[because t=sqrtx]`
`=(cos(sqrt(sin sqrtx)))/(4sqrtxsqrt(sinsqrtx)).cosx.`
