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

Math
Differentiate both sides of the equation.
Differentiate using the Power Rule which states that is where .
Differentiate the right side of the equation.
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Use the Binomial Theorem.
Simplify each term.
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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 .
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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 .
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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.
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Apply the distributive property.
Apply the distributive property.
Combine terms.
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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.
Solve for .
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Rewrite the equation as .
Simplify .
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Add and .
Subtract from .
Add and .
Factor out of .
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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.
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Divide each term in by .
Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Replace with .
Find dx/dy y=x(x-4)^3


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