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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Differentiate using the Power Rule which states that is where .
Step 4.2
Multiply by .
Step 4.3
By the Sum Rule, the derivative of with respect to is .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Add and .
Step 4.6
Differentiate using the Power Rule which states that is where .
Step 4.7
Multiply by .
Step 5
Step 5.1
Simplify the numerator.
Step 5.1.1
Simplify each term.
Step 5.1.1.1
Expand using the FOIL Method.
Step 5.1.1.1.1
Apply the distributive property.
Step 5.1.1.1.2
Apply the distributive property.
Step 5.1.1.1.3
Apply the distributive property.
Step 5.1.1.2
Simplify each term.
Step 5.1.1.2.1
Multiply by .
Step 5.1.1.2.2
Multiply by .
Step 5.1.1.2.3
Multiply by by adding the exponents.
Step 5.1.1.2.3.1
Move .
Step 5.1.1.2.3.2
Multiply by .
Step 5.1.2
Combine the opposite terms in .
Step 5.1.2.1
Subtract from .
Step 5.1.2.2
Add and .
Step 5.2
Reorder terms.