dyĐ°Ńysin (VSin x+ cosx),find

1.	dyĐ°Ńysin (VSin x+ cosx),find
Answer» Let w = √( sin x + cos x ) , V = sin x + cos x So y = sin w w = √v and V = sin x + cos x dy / dw = cos w dw / dv = 1/(2√v) and dv/ dx = cos x – sin x Thus dy / dx = ( dy / dw ) × ( dw / dv ) × ( dv / dx ) = cos w × 1/(2√v) × ( cos x – sin x) = cos [√( sin x + cos x ) ] × 1/ [ 2 √(sin x +cos x) ] × ( cos x – sin x)

Answer»

Let w = √( sin x + cos x ) , V = sin x + cos x

So y = sin w w = √v and V = sin x + cos x

dy / dw = cos w dw / dv = 1/(2√v) and dv/ dx = cos x – sin x

Thus dy / dx = ( dy / dw ) × ( dw / dv ) × ( dv / dx )

= cos w × 1/(2√v) × ( cos x – sin x)

= cos [√( sin x + cos x ) ] × 1/ [ 2 √(sin x +cos x) ] × ( cos x – sin x)

Discussion