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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
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 3
Differentiate using the Exponential Rule which states that is where =.
Step 4
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 5
Differentiate using the Exponential Rule which states that is where =.
Step 6
Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Multiply by .
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Simplify the numerator.
Step 7.2.1
Simplify each term.
Step 7.2.1.1
Expand using the FOIL Method.
Step 7.2.1.1.1
Apply the distributive property.
Step 7.2.1.1.2
Apply the distributive property.
Step 7.2.1.1.3
Apply the distributive property.
Step 7.2.1.2
Simplify and combine like terms.
Step 7.2.1.2.1
Simplify each term.
Step 7.2.1.2.1.1
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.1.2
Multiply by .
Step 7.2.1.2.1.3
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.1.4
Multiply by by adding the exponents.
Step 7.2.1.2.1.4.1
Move .
Step 7.2.1.2.1.4.2
Use the power rule to combine exponents.
Step 7.2.1.2.1.4.3
Add and .
Step 7.2.1.2.1.5
Multiply by .
Step 7.2.1.2.1.6
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.1.7
Multiply by by adding the exponents.
Step 7.2.1.2.1.7.1
Move .
Step 7.2.1.2.1.7.2
Multiply by .
Step 7.2.1.2.1.8
Multiply by .
Step 7.2.1.2.1.9
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.1.10
Multiply by .
Step 7.2.1.2.2
Subtract from .
Step 7.2.1.2.2.1
Move .
Step 7.2.1.2.2.2
Subtract from .
Step 7.2.1.3
Multiply by .
Step 7.2.1.4
Multiply by .
Step 7.2.1.5
Expand using the FOIL Method.
Step 7.2.1.5.1
Apply the distributive property.
Step 7.2.1.5.2
Apply the distributive property.
Step 7.2.1.5.3
Apply the distributive property.
Step 7.2.1.6
Simplify each term.
Step 7.2.1.6.1
Rewrite using the commutative property of multiplication.
Step 7.2.1.6.2
Multiply by .
Step 7.2.1.6.3
Multiply .
Step 7.2.1.6.3.1
Multiply by .
Step 7.2.1.6.3.2
Multiply by .
Step 7.2.1.6.4
Rewrite using the commutative property of multiplication.
Step 7.2.1.6.5
Multiply by by adding the exponents.
Step 7.2.1.6.5.1
Move .
Step 7.2.1.6.5.2
Use the power rule to combine exponents.
Step 7.2.1.6.5.3
Add and .
Step 7.2.1.6.6
Multiply by .
Step 7.2.1.6.7
Multiply by .
Step 7.2.2
Combine the opposite terms in .
Step 7.2.2.1
Subtract from .
Step 7.2.2.2
Add and .
Step 7.2.3
Add and .
Step 7.3
Reorder terms.
Step 7.4
Factor out of .
Step 7.5
Factor out of .
Step 7.6
Factor out of .
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
Rewrite as .
Step 7.12
Move the negative in front of the fraction.
Step 7.13
Reorder factors in .