Differentiate both sides of the equation.

Differentiate using the Power Rule which states that is where .

Use the Binomial Theorem.

Simplify each term.

Multiply by .

Raise to the power of .

Multiply by .

Raise to the power of .

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

By the Sum Rule, 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 .

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 .

Multiply by .

Rewrite as .

Since is constant with respect to , the derivative of with respect to is .

Rewrite as .

Since is constant with respect to , the derivative of with respect to is .

Add and .

Rewrite as .

Simplify.

Apply the distributive property.

Apply the distributive property.

Combine terms.

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Move to the left of .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

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

Rewrite the equation as .

Simplify .

Add and .

Subtract from .

Add and .

Factor out of .

Factor out of .

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 .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Replace with .

Find dx/dy y=x(x-4)^3