Differentiate both sides of the equation.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Differentiate using the Product Rule which states that is where and .

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 .

Differentiate using the Power Rule which states that is where .

Move to the left of .

Move to the left of .

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 .

Simplify.

Apply the distributive property.

Remove unnecessary parentheses.

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.

Add to 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 .

Cancel the common factor.

Rewrite the expression.

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.

Factor out of .

Factor out of .

Raise to the power of .

Factor out of .

Factor out of .

Cancel the common factor of and .

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Reorder terms.

Cancel the common factor.

Rewrite the expression.

Simplify the expression.

Move to the left of .

Move the negative in front of the fraction.

Replace with .

Find dy/dx x^2y^2-xy=8