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यदि `y= sin (sqrt (sin x + cos x ) ),` तब `(dy)/(dx) ` का मान ज्ञात कीजिए|

Answer» `y= sin (sqrt (sin x + cos x ) ),`
माना ` (sin x +cos x ) =t` और ` sqrt t =u`
` therefore y= sin u,u =sqrt (t),t =sin x + cos x `
` " "=(dy)/(du )= cos u ,""(du)/(dt) =(1)/(2) t(-1//2) =(1)/(2sqrt (t))`
तथा ` (dt)/(dx) = (cos x - sin x ) `
हम जानते है की ` (dy)/(dx) =((dy)/(du)xx(du)/(dt)xx(dt)/(dx))`
` =[ cos uxx(1)/(2sqrt (t))xx(cos x- sin x ) ]`
` =(cos sqrtt )/(2sqrt t ) (cos x - sin x ) `
` =(cos sqrt (sinx +cos x) ) /(2 sqrt( sin x+ cos x ))*(cos x -sin x ) `


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