# Find dx/dy y=x(x-4)^3 Differentiate both sides of the equation.
Differentiate using the Power Rule which states that is where .
Differentiate the right side of the equation.
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 .
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.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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.
Solve for .
Rewrite the equation as .
Simplify .
Subtract from .
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