If `sin(x y)+y/x=x^2-y^2` , find `(dy)/(dx)` .

Answer

N/a

Explanation

We have, ` sin(xy)+x/y=x^(2)-y`
On differenting both sides w.r.t.x, we get
`d/dx (sinxy)+d/dx (x/y)=d/(dx)x^(2) - d/(dx)y`
`rArr cos xy. (d)/(dx)(xy) + (y.(d)/(dx)x-x.(d)/(dx)y)/(y^(2)) = 2x - (dy)/(dx)`
`rArr cos xy. [x.(d)/(dx)y+y.(d)/(dx).x]+(y-x'(dy)/(dx))/(y^(2)) = 2x- (dy)/(dx)`
`rArr x cos xy. (dy)/(dx) + ycosxy+(y)/(y^(2))-(x)/(y^(2)) (dy)/(dx) = 2x - (dy)/(dx)`
`rArr (dy)/(dx) [xcosxy-(x)/(y^(2))+1] = 2x-ycosxy-(y)/(y^(2))`
`:. (dy)/(dx) = [(2xy-y^(2)cosxy-1)/(y)][(y^(2))/(xy^(2)cosxy-x+y^(2))]`
`= ((2xy-y^(2)cosxy-1)y)/((xy^(2)cosxy-x+y^(2)))`