Calculus Examples

Find the Derivative - d/dx y=(x^2+9)/x
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Add and .
Step 3
Raise to the power of .
Step 4
Raise to the power of .
Step 5
Use the power rule to combine exponents.
Step 6
Add and .
Step 7
Differentiate using the Power Rule which states that is where .
Step 8
Multiply by .
Step 9
Simplify.
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Step 9.1
Apply the distributive property.
Step 9.2
Simplify the numerator.
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Step 9.2.1
Multiply by .
Step 9.2.2
Subtract from .
Step 9.3
Simplify the numerator.
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Step 9.3.1
Rewrite as .
Step 9.3.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .