

InterviewSolution
Saved Bookmarks
1. |
If `y=e^(sqrt(cotx))`, find `(dy)/(dx)`. |
Answer» 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)).` |
|