hey here is one solution
given that y=sin x
dy/dx = cos x
dx/dy = sec x
now let t= cos 7 x
then d (cos 7 x)/ dy = (dt/dx) (dy/dx)
= (-7 cos 6 x sin x) (sec x)
= -7 cos 5 x sin x
now let u = -7 cos 5 x sin x
thrfore d2 (cos 7 x) / dy2 = du/ dy
= (du/dx) (dx/dy)
= (-7cos 6 x + 35 cos4 x sin2 x) (sec x)
= -7cos 5 x + 35 cos3 x sin2 x
pls tell if m wrong anywhere!!!