Q. 123.7( 76 Votes )

Find dy/dx of the functions.

xy + yx = 1

Answer :

Given: xy + yx = 1

Let y= xy + yx = 1


Let u = xy and v = yx


Then, u + v = 1



For, u = xy


Taking log on both sides, we get


Log u =log xy


log u = y.log(x)


Now, differentiate both sides with respect to x






For, v = yx


Taking log on both sides, we get


Log v =log yx


log v = x.log(y)


Now, differentiate both sides with respect to x











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