यदि `sin(xy)+x/y=x^(2)-y` हो,तो `(dy)/(dx)` ज्ञात कीजिए ।

Explanation

`sin(xy)+x/y=x^(2)-y`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`d/(dx)sin(xy)+d/(dx)(x/y)=d/(dx)(x^(2))-(dy)/(dx)`
`rArrcos(xy)d/(dx)(xy)+(y-x(dy)/(dx))/(y^(2))=2x-(dy)/(dx)`
`rArrcos(xy)(x(dy)/(dx)+y)+1/y-x/(y^(2))(dy)/(dx)=2x-(dy)/(dx)`
`rArrxcos(xy)(dy)/(dx)+ycos(xy)+1/y-x/(y^(2))(dy)/(dx)=2x-(dy)/(dx)`
`rArr[xcos(xy)-x/(y^(2))+1](dy)/(dx)`
`=2x-1/y-ycos(xy)`
`rArr[xy^(2)cos(xy)-x+y^(2)](dy)/(dx)`
`=[2x-1/y-ycos(xy)]y^(2)`
`rArr[xy^(2)cos(xy)-x+y^(2)](dy)/(dx)`
`=[2xy^(2)-y-y^(3)cos(xy)]` ltbr gt`rArr(dy)/(dx)=(2xy^(2)-y-y^(3)cos(xy))/(xy^(2)cos(xy)-x+y^(2))`