SOLUTION: Let {{{ ln(x-y) = xy }}} (a). Find {{{ dy/dx }}} at (1,0) (b). Write the equation of the tangent line to the graph at (1,0) Thank you

Algebra ->  Equations -> SOLUTION: Let {{{ ln(x-y) = xy }}} (a). Find {{{ dy/dx }}} at (1,0) (b). Write the equation of the tangent line to the graph at (1,0) Thank you      Log On


   

Question 991364: Let +ln%28x-y%29+=+xy+
(a). Find +dy%2Fdx+ at (1,0)
(b). Write the equation of the tangent line to the graph at (1,0)

Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Differentiate implicitly,
%28dx-dy%29%2F%28x-y%29=xdy%2Bydx
dx-dy=%28x-y%29xdy%2B%28x-y%29ydx
-%28x-y%29xdy-dy=%28x-y%29ydx-dx
%28-%28x-y%29x-1%29dy=%28%28x-y%29y-1%29dx
dy%2Fdx=%28%28x-y%29y-1%29%2F%28-%28x-y%29x-1%29
So then,
dy%2Fdx=%28%281-0%290-1%29%2F%28-%281-0%291-1%29
dy%2Fdx=%28-1%29%2F%28-1-1%29
dy%2Fdx=-1%2F%28-2%29
dy%2Fdx=1%2F2
Use the point-slope form of the tangent line,
y-0=%281%2F2%29%28x-1%29
y=%281%2F2%29x-1%2F2
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