# Find dy/dx 9xy+y^2=2x+y

Differentiate both sides of the equation.
Differentiate the left side of the equation.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Evaluate .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Simplify.
Apply the distributive property.
Reorder terms.
Differentiate the right side of the equation.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite as .
Reform the equation by setting the left side equal to the right side.
Solve for .
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Replace with .
Find dy/dx 9xy+y^2=2x+y

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