Calculus Examples

Find the Derivative Using Quotient Rule - d/dx
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 3
Evaluate .
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Differentiate.
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Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Add and .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
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Step 5.3.1
Simplify each term.
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Step 5.3.1.1
Expand using the FOIL Method.
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Step 5.3.1.1.1
Apply the distributive property.
Step 5.3.1.1.2
Apply the distributive property.
Step 5.3.1.1.3
Apply the distributive property.
Step 5.3.1.2
Simplify each term.
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Step 5.3.1.2.1
Rewrite using the commutative property of multiplication.
Step 5.3.1.2.2
Multiply by by adding the exponents.
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Step 5.3.1.2.2.1
Move .
Step 5.3.1.2.2.2
Multiply by .
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Step 5.3.1.2.2.2.1
Raise to the power of .
Step 5.3.1.2.2.2.2
Use the power rule to combine exponents.
Step 5.3.1.2.2.3
Add and .
Step 5.3.1.2.3
Move to the left of .
Step 5.3.1.2.4
Multiply by .
Step 5.3.1.2.5
Multiply by .
Step 5.3.1.3
Multiply by .
Step 5.3.1.4
Multiply by .
Step 5.3.1.5
Multiply by .
Step 5.3.2
Combine the opposite terms in .
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Step 5.3.2.1
Add and .
Step 5.3.2.2
Add and .
Step 5.3.3
Subtract from .
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