Find dx/dy y=(x^2-3x+2)/(x^7-2)

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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Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Differentiate using the Quotient Rule which states that is where and .
Differentiate using the Product Rule which states that is where and .
By the Sum Rule, the derivative of with respect to is .
Rewrite as .
Since is constant with respect to , the derivative of with respect to is .
Add and .
By the Sum Rule, the derivative of with respect to is .
Rewrite as .
Differentiate.
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Since is constant with respect to , the derivative of with respect to is .
Add 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 .
Simplify the expression.
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Add and .
Multiply by .
Simplify.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
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Rewrite as .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify each term.
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Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite using the commutative property of multiplication.
Multiply by .
Multiply by .
Multiply by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by by adding the exponents.
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Move .
Multiply by .
Multiply by .
Multiply by .
Add and .
Apply the distributive property.
Simplify.
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Multiply by by adding the exponents.
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Move .
Use the power rule to combine exponents.
Add and .
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Apply the distributive property.
Combine terms.
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Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Reorder terms.
Reform the equation by setting the left side equal to the right side.
Solve for .
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Rewrite the equation as .
Multiply both sides of the equation by .
Simplify .
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Remove parentheses.
Add and .
Subtract from .
Subtract from .
Add and .
Subtract from .
Add and .
Simplify .
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Simplify the expression.
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Multiply by .
Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Move to the left of .
Multiply by .
Subtract from .
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 .
Factor out of .
Factor out of .
Reorder terms.
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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Combine the numerators over the common denominator.
Simplify the numerator.
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Rewrite as .
Let . Substitute for all occurrences of .
Factor using the perfect square rule.
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Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Replace all occurrences of with .
Simplify with factoring out.
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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 .
Rewrite as .
Factor out of .
Rewrite negatives.
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Rewrite as .
Move the negative in front of the fraction.
Replace with .
Find dx/dy y=(x^2-3x+2)/(x^7-2)

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