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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 3
Differentiate using the Product Rule which states that is where and .
Step 4
Differentiate using the Exponential Rule which states that is where =.
Step 5
Step 5.1
Differentiate using the Power Rule which states that is where .
Step 5.2
Multiply by .
Step 5.3
By the Sum Rule, the derivative of with respect to is .
Step 5.4
Differentiate using the Power Rule which states that is where .
Step 6
Differentiate using the Exponential Rule which states that is where =.
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Simplify the numerator.
Step 7.3.1
Simplify each term.
Step 7.3.1.1
Expand using the FOIL Method.
Step 7.3.1.1.1
Apply the distributive property.
Step 7.3.1.1.2
Apply the distributive property.
Step 7.3.1.1.3
Apply the distributive property.
Step 7.3.1.2
Simplify each term.
Step 7.3.1.2.1
Rewrite using the commutative property of multiplication.
Step 7.3.1.2.2
Multiply by by adding the exponents.
Step 7.3.1.2.2.1
Move .
Step 7.3.1.2.2.2
Multiply by .
Step 7.3.1.2.3
Rewrite using the commutative property of multiplication.
Step 7.3.1.2.4
Rewrite using the commutative property of multiplication.
Step 7.3.1.2.5
Multiply by by adding the exponents.
Step 7.3.1.2.5.1
Move .
Step 7.3.1.2.5.2
Use the power rule to combine exponents.
Step 7.3.1.2.5.3
Add and .
Step 7.3.1.2.6
Rewrite using the commutative property of multiplication.
Step 7.3.1.2.7
Multiply by by adding the exponents.
Step 7.3.1.2.7.1
Move .
Step 7.3.1.2.7.2
Use the power rule to combine exponents.
Step 7.3.1.2.7.3
Add and .
Step 7.3.1.3
Simplify each term.
Step 7.3.1.3.1
Multiply by .
Step 7.3.1.3.2
Multiply .
Step 7.3.1.3.2.1
Multiply by .
Step 7.3.1.3.2.2
Multiply by .
Step 7.3.1.4
Expand using the FOIL Method.
Step 7.3.1.4.1
Apply the distributive property.
Step 7.3.1.4.2
Apply the distributive property.
Step 7.3.1.4.3
Apply the distributive property.
Step 7.3.1.5
Simplify each term.
Step 7.3.1.5.1
Multiply by .
Step 7.3.1.5.2
Multiply by .
Step 7.3.1.5.3
Multiply by by adding the exponents.
Step 7.3.1.5.3.1
Move .
Step 7.3.1.5.3.2
Use the power rule to combine exponents.
Step 7.3.1.5.3.3
Add and .
Step 7.3.2
Combine the opposite terms in .
Step 7.3.2.1
Add and .
Step 7.3.2.2
Add and .
Step 7.3.2.3
Reorder the factors in the terms and .
Step 7.3.2.4
Add and .
Step 7.3.2.5
Add and .
Step 7.4
Reorder terms.
Step 7.5
Factor out of .
Step 7.6
Rewrite as .
Step 7.7
Factor out of .
Step 7.8
Factor out of .
Step 7.9
Factor out of .
Step 7.10
Factor out of .
Step 7.11
Factor out of .
Step 7.12
Rewrite as .
Step 7.13
Move the negative in front of the fraction.
Step 7.14
Reorder factors in .