Find dy/dx xy+x+y=x^2y^2

Problem

x*y+x+y=x2*y2

Solution

1. Differentiate both sides with respect to x treating y as a function of x and applying the product rule where necessary.

d()/d(x)*(x*y+x+y)=d()/d(x)*(x2*y2)

2. Apply the product rule to the terms x*y and x2*y2

(xd(y)/d(x)+y)+1+d(y)/d(x)=x2*(2*yd(y)/d(x))+y2*(2*x)

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

xd(y)/d(x)+d(y)/d(x)−2*x2*yd(y)/d(x)=2*x*y2−y−1

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

d(y)/d(x)*(x+1−2*x2*y)=2*x*y2−y−1

5. Solve for d(y)/d(x) by dividing both sides by the expression in the parentheses.

d(y)/d(x)=(2*x*y2−y−1)/(x+1−2*x2*y)

Final Answer

d(y)/d(x)=(2*x*y2−y−1)/(x+1−2*x2*y)

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