Find dy/dx 1-xy=x-y

Problem

1−x*y=x−y

Solution

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

d(1−x*y)/d(x)=d(x−y)/d(x)

2. Apply the product rule to the term x*y on the left side and differentiate the terms on the right side.

0−(xd(y)/d(x)+y⋅1)=1−d(y)/d(x)

3. Distribute the negative sign and simplify the expression.

−xd(y)/d(x)−y=1−d(y)/d(x)

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

d(y)/d(x)−xd(y)/d(x)=1+y

5. Factor out d(y)/d(x) from the left side of the equation.

d(y)/d(x)*(1−x)=1+y

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

d(y)/d(x)=(1+y)/(1−x)

Final Answer

d(y)/d(x)=(1+y)/(1−x)

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