Calculus Examples

Find the Derivative - d/dx (x^2)/(x^2-9)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
Differentiate using the Power Rule which states that is where .
Step 2.2
Move to the left of .
Step 2.3
By the Sum Rule, the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.6
Simplify the expression.
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Step 2.6.1
Add and .
Step 2.6.2
Multiply by .
Step 3
Raise to the power of .
Step 4
Use the power rule to combine exponents.
Step 5
Add and .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Simplify the numerator.
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Step 6.3.1
Simplify each term.
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Step 6.3.1.1
Multiply by by adding the exponents.
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Step 6.3.1.1.1
Move .
Step 6.3.1.1.2
Multiply by .
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Step 6.3.1.1.2.1
Raise to the power of .
Step 6.3.1.1.2.2
Use the power rule to combine exponents.
Step 6.3.1.1.3
Add and .
Step 6.3.1.2
Multiply by .
Step 6.3.2
Combine the opposite terms in .
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Step 6.3.2.1
Subtract from .
Step 6.3.2.2
Add and .
Step 6.4
Move the negative in front of the fraction.
Step 6.5
Simplify the denominator.
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Step 6.5.1
Rewrite as .
Step 6.5.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 6.5.3
Apply the product rule to .