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

Math
Differentiate both sides of the equation.
Differentiate the left side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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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 .
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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 .
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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 .
Multiply by .
Move to the left of .
Reorder terms.
Differentiate the right side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Rewrite as .
Evaluate .
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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.
Solve for .
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Subtract from both sides of the equation.
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Factor out of .
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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 .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Simplify each term.
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Move the negative in front of the fraction.
Move the negative in front of the fraction.
Combine into one fraction.
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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

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