`e^("sin x")` का अवलन गुणांक `sqrt("sin x")` के सपेक्ष ज्ञात कीजिये|

Explanation

`y_(1)=e^(sin x)`
`(d y _(1))/(dx)=e^(sin x )(d)/(dx) (sin x)`
`(dy_(1))/(dx)=e^(sin x) (cos x) ` ...(i)
`y_(2) = sqrt( sin x ) `
`(dy_(2))/(dx)=(1)/(2)(sin x)^(1/2-1) (d)/(dx)(sin x)`
`(dy_(2))/(dx)=(cos x ) /(2sqrt(sin x)) ` ...(ii)
`(dy_(1))/(dy_(2))=(dx)/((dy_(2))/(dx))=(e^(sin x).cos x)/((cos x)/(2 sqrt(sin x)))`
`=2sqrt(sin x). e^(sin x)`