If `cos(x+y)=y sin x,` find `(dy)/(dx).`

1.	If `cos(x+y)=y sin x,` find `(dy)/(dx).`
Answer» Given: `cos(x+y)=y sin x.` On differentiating both sides of (i) w.r.t. x, we get `-sin(x+y).(d)/(dx)(x+y)=y cos+sinx.(dy)/(dx)` `rArr-sin(x+y)(1+(dy)/(dx))=y cos x+sin x.(dy)/(dx)` `rArr{sin(x+y)+sinx}.(dy)/(dx)=-{sin(x+y)+ycosx}` `rArr(dy)/(dx)=(-{sin(x+y)+ycosx})/({sin(x+y)+sinx}).`

Discussion

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