Engineering Board Exam Reviewer · Implicit Differentiation · hard

Find dy/dx if xy=yx (for x,y>0).

1. y ≤ft(x y + y )/x ≤ft(- x + y x )
2. y y - y/x x - x
3. y ≤ft(x y - y )/x ≤ft(x + y x )
4. y ≤ft(x y - y )/x ≤ft(- x + y x )

Answer

D. y ≤ft(x y - y )/x ≤ft(- x + y x )

Solution

Take logarithms: y x=x y. Differentiate: y' x+ yx= y+xy'/y. Then y'≤ft( x- xy )= y- yx, so dy/dx=y(x y-y)/x(y x-x).

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