Find dy/dx xy+x=2

Problem

x*y+x=2

Solution

1. Differentiate both sides of the equation with respect to x

d()/d(x)*(x*y+x)=d(2)/d(x)

2. Apply the product rule to the term x*y where (d(x)*y)/d(x)=xd(y)/d(x)+yd(x)/d(x)

xd(y)/d(x)+y(1)+1=0

3. Simplify the equation by combining the constant terms.

xd(y)/d(x)+y+1=0

4. Isolate the term containing d(y)/d(x) by subtracting y+1 from both sides.

xd(y)/d(x)=−y−1

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

d(y)/d(x)=(−y−1)/x

Final Answer

d(y)/d(x)=−(y+1)/x

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