Differentiate both sides 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 .

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 .

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.

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 .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Simplify each term.

Move the negative in front of the fraction.

Move the negative in front of the fraction.

Simplify terms.

Combine the numerators over the common denominator.

Factor out of .

Factor out of .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

Replace with .

Find dy/dx x^2+xy+y^2=27