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

Differentiate both sides of the equation.
Differentiate the left side of the equation.
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
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 .
Since is constant with respect to , the derivative of with respect to is .
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 .
Multiply by .
Simplify.
Apply the distributive property.
Remove unnecessary parentheses.
Reorder terms.
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Solve for .
Move all terms not containing to the right side of the equation.
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 .
Divide each term by and simplify.
Divide each term in by .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Simplify each term.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Replace with .
Find dy/dx x+2xy-y^2=2