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 Power Rule which states that is where .

Rewrite as .

Move to the left of .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

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 .

Move to the left of .

Reorder terms.

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

Rewrite as .

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 .

Reform the equation by setting the left side equal to the right side.

Subtract from both sides of the equation.

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 .

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.

Combine into one fraction.

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Replace with .

Find dx/dy xy^4+x^5y=x+8y