# Find dx/dy y=(x^2-3x+2)/(x^7-2) Differentiate both sides of the equation.
Differentiate using the Power Rule which states that is where .
Differentiate the right side of the equation.
Factor using the AC method.
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 .
By the Sum Rule, the derivative of with respect to is .
Rewrite as .
Differentiate.
Since is constant with respect to , the derivative of with respect to is .
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 .
Simplify the expression.
Multiply by .
Simplify.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Rewrite as .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite using the commutative property of multiplication.
Multiply by .
Multiply by .
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Apply the distributive property.
Combine terms.
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 .
Rewrite the equation as .
Multiply both sides of the equation by .
Simplify .
Remove parentheses.
Subtract from .
Subtract from .
Subtract from .
Simplify .
Simplify the expression.
Multiply by .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
Move to the left of .
Multiply by .
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 .
Factor out of .
Factor out of .
Reorder terms.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Combine the numerators over the common denominator.
Simplify the numerator.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the perfect square rule.
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.
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.
Rewrite as .
Move the negative in front of the fraction.
Replace with .
Find dx/dy y=(x^2-3x+2)/(x^7-2)     