Find dy/dx x^2+5x+9xy-y^2=4

Problem

x2+5*x+9*x*y−y2=4

Solution

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

d(x2)/d(x)+(d(5)*x)/d(x)+(d(9)*x*y)/d(x)−d(y2)/d(x)=d(4)/d(x)

2. Apply the product rule to the term 9*x*y and the chain rule to the term y2

2*x+5+9*y+9*xd(y)/d(x)−2*yd(y)/d(x)=0

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

9*xd(y)/d(x)−2*yd(y)/d(x)=−2*x−5−9*y

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

d(y)/d(x)*(9*x−2*y)=−2*x−5−9*y

5. Solve for d(y)/d(x) by dividing both sides by the expression (9*x−2*y)

d(y)/d(x)=(−2*x−5−9*y)/(9*x−2*y)

Final Answer

d(y)/d(x)=(−2*x−5−9*y)/(9*x−2*y)

Want more problems? Check here!