Posted by Anamika on Tuesday, December 11, 2012 at 6:59am.
looks like triple product rule
recall
d(uvw) = uvw' + uwv' + vwu'
I will also assume that you meant ln(x+y)
xy ln(x+y) = 1
xy(1/(x+y)) * (1 + dy/dx) + x ln(x+y) dy/dx + y ln(x+y) = 0
expand the first part to get at the dy/dx
xy(1/(x+y)) + dy/dx xy(1/(x+y)) + dy/dx (x ln(x+y)) = -y ln(x+y) - xy(1/(x+y))
dy/dx [xy(1/(x+y)) + (x ln(x+y)) ] = -y ln(x+y) - xy(1/(x+y))
dy/dx = (-y ln(x+y) - xy(1/(x+y))) / [xy(1/(x+y)) + (x ln(x+y)) ]
leave it like that or simplify as needed.
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