Find dy/dx x+y=xy

Problem

x+y=x*y

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x and applying the chain rule.

d()/d(x)*(x+y)=d()/d(x)*(x*y)

2. Apply the sum rule on the left side and the product rule on the right side.

1+d(y)/d(x)=xd(y)/d(x)+y(1)

3. Group all terms containing d(y)/d(x) on one side of the equation and the remaining terms on the other side.

d(y)/d(x)−xd(y)/d(x)=y−1

4. Factor out the common term d(y)/d(x) from the left side.

d(y)/d(x)*(1−x)=y−1

5. Solve for d(y)/d(x) by dividing both sides by (1−x)

d(y)/d(x)=(y−1)/(1−x)

Final Answer

d(y)/d(x)=(y−1)/(1−x)

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