Given: `y=e^(sqrt(cotx))`.
Putting `cotx=t and sqrt(cotx)=sqrt(t)=u`, we get
`y=e^(u),u=sqrt(t)and t=cotx`
`rArr(dy)/(dx)=e^(u),(du)/(dt)=(1)/(2)t^(-1//2)=(1)/(2sqrtt)and (dt)/(dx)=-"cosec"^(2)x`
`rArr(dy)/(dx)=((dy)/(du)xx(du)/(dt)xx(dt)/(dx))`
`={e^(u).(1)/(2sqrtt).(-"cosec"^(2)x)}=e^(sqrt(cotx)).(1)/(2sqrt(cotx)).(-"cosec"^(2)x)`
`=((-"cosec"^(2)x)e^(sqrt(cotx)))/(2sqrt(cotx)).`
