Let y=cos(sin^-1(2w))y=cos(sin−1(2w))
Let u=sin^-1(2w)u=sin−1(2w)
sinu=2wsinu=2w
(du)/(dw)cosu=2dudwcosu=2
(du)/(dw)=2/cosududw=2cosu
cos^2u+sin^2u=1cos2u+sin2u=1
cos^2u=1-sin^2u=1-(2w)^2cos2u=1−sin2u=1−(2w)2
cosu=sqrt(1-4w^2)cosu=√1−4w2
(du)/(dw)=2/sqrt(1-4w^2)dudw=2√1−4w2
d/(dw)cos(u)=-sin(u)xx(du)/(dw)ddwcos(u)=−sin(u)×dudw
=-sin(sin^-1(2w))xx2/(sqrt(1-4w^2))=−sin(sin−1(2w))×2√1−4w2
=-(4w)/(sqrt(1-4w^2))=−4w√1−4w2