`e^(sqrt(cot x))` का अवलंकन कीजिएः।

Explanation

माना `y=e^(sqrt(cot x))`
cot x=t रखने पर
`Rightarrow sqrt(cot x)=sqrtt=u("माना")`
`y=e^(u), u=sqrtt "व" t=cot x`
अंत: `(dy)/(du)=e^(u), (du)/(dt)=(1)/(2), t^(-1//2)=(1)/(2sqrtt), (dt)/(dx)=-cosec^(2)x`
अंत: `(dy)/(dx)=(dy)/(du)xx(du)/(dt)xx(dt)/(dx)`
`=-(1)/(2)("cosec"^(2)x)/(sqrtt).e^(u)`
`=("cosec"^(2)x)/(2sqrtt).e^(sqrtt)`
`=-("cosec"^(2)x)/(2cotx).e^(cot t)`