SOLUTION: if x+y=xy, then dy/dx is?

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Question 266664: if x+y=xy, then dy/dx is?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We use implicit differentiation here. On the left, it is regular derivatives, but on the right we need to the product rule. we get
(i) 1+%2B+1dy%2Fdx+=+x%28dy%2Fdx%29+%2B+y
step 1 - subtract 1 (dy/dx) from both sides and then subtract y from both sides to get
(ii) 1-+y+=+x%28dx%2Fdy%29+-+1%28dy%2Fdx%29
step 2 - factor out the dy/dx to get
(iii) 1+-+y+=+%28dy%2Fdx%29+%28x-1%29
step 3 - divide by x-1 to get
(iv) %281-y%29%2F%28x-1%29+=+%28dy%2Fdx%29