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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Simplify the expression.
Step 2.6.1
Multiply by .
Step 2.6.2
Move to the left of .
Step 2.7
By the Sum Rule, the derivative of with respect to is .
Step 2.8
Since is constant with respect to , the derivative of with respect to is .
Step 2.9
Differentiate using the Power Rule which states that is where .
Step 2.10
Multiply by .
Step 2.11
Differentiate using the Power Rule which states that is where .
Step 3
Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Simplify the numerator.
Step 3.3.1
Simplify each term.
Step 3.3.1.1
Multiply by .
Step 3.3.1.2
Simplify each term.
Step 3.3.1.2.1
Multiply by .
Step 3.3.1.2.2
Multiply by .
Step 3.3.1.3
Expand using the FOIL Method.
Step 3.3.1.3.1
Apply the distributive property.
Step 3.3.1.3.2
Apply the distributive property.
Step 3.3.1.3.3
Apply the distributive property.
Step 3.3.1.4
Simplify and combine like terms.
Step 3.3.1.4.1
Simplify each term.
Step 3.3.1.4.1.1
Multiply by .
Step 3.3.1.4.1.2
Multiply by .
Step 3.3.1.4.1.3
Rewrite using the commutative property of multiplication.
Step 3.3.1.4.1.4
Multiply by by adding the exponents.
Step 3.3.1.4.1.4.1
Move .
Step 3.3.1.4.1.4.2
Multiply by .
Step 3.3.1.4.1.5
Multiply by .
Step 3.3.1.4.1.6
Multiply by .
Step 3.3.1.4.2
Add and .
Step 3.3.2
Add and .
Step 3.3.3
Subtract from .
Step 3.4
Simplify the denominator.
Step 3.4.1
Factor out of .
Step 3.4.1.1
Factor out of .
Step 3.4.1.2
Raise to the power of .
Step 3.4.1.3
Factor out of .
Step 3.4.1.4
Factor out of .
Step 3.4.2
Apply the product rule to .