InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Differentiate `sqrt(cot^(-1)sqrtx)`, w.r.t. x. |
|
Answer» Let `y=sqrt(cot^(-1)sqrtx)`. Putting `sqrtx=t and cot^(-1)sqrtx=cot^(-1)sqrtx=u`, we get `y=sqrtu,` where `u=cot^(-1)t and t=sqrtx`. Now, `y=sqrtu rArr (dy)/(du)=(1)/(2)u^(-1//2)=(1)/(2sqrtu),` `u=cot^(-1)t rArr (du)/(dt)=(-1)/((1+t^(2)))`. And, `t=sqrtx rArr (dt)/(dx)=(1)/(2)x^(-1//2)=(1)/(2sqrtx)`. `therefore(dy)/(dx)=((dy)/(du)xx(du)/(dt)xx(dt)/(dx))=(-1)/(4sqrtu(1+t^(2))sqrtx)` `" "=(-1)/(4(sqrt(cot^(-1)t))(1+t^(2))sqrtx)" "[because u=cot^(-1)t]` `" "=(-1)/(4(sqrt(cot^(-1)sqrtx))(1+x)sqrtx)" "[because t=sqrtx].` |
|