sin x+y+cos x+y=1d dxsin x+y+cos x+y=0d dxsin x+y+d dxcos x+y=0cos x+y×d dxx+y-sin x+y×d dxx+y=0cos x+y-sin x+yd dxx+y=0cos x+y-sin x+y1+dydx=0cos x+y-sin x+y+cos x+y-sin x+ydydx=0cos x+y-sin x+ydydx=-cos x+y-sin x+ydydx=-cos x+y-sin x+ycos x+y-sin x+ydydx=-1

Differentiate wrt x

\sin (x + y) + \cos (x + y) = 1 \frac{d}{d x} \{\sin (x + y) + \cos (x + y)\} = 0 \frac{d}{d x} \sin (x + y) + \frac{d}{d x} \cos (x + y) = 0 \cos (x + y) \times \frac{d}{d x} (x + y) - \sin (x + y) \times \frac{d}{d x} (x + y) = 0 (\cos (x + y) - \sin (x + y)) \frac{d}{d x} (x + y) = 0 (\cos (x + y) - \sin (x + y)) \{1 + \frac{d y}{d x}\} = 0 (\cos (x + y) - \sin (x + y)) + (\cos (x + y) - \sin (x + y)) \frac{d y}{d x} = 0 (\cos (x + y) - \sin (x + y)) \frac{d y}{d x} = - (\cos (x + y) - \sin (x + y)) \frac{d y}{d x} = - \frac{(\cos (x + y) - \sin (x + y))}{(\cos (x + y) - \sin (x + y))} \frac{d y}{d x} = - 1

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