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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4
Simplify the expression.
Step 3.4.1
Add and .
Step 3.4.2
Multiply by .
Step 3.5
By the Sum Rule, the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.8
Simplify the expression.
Step 3.8.1
Add and .
Step 3.8.2
Multiply by .
Step 3.9
By the Sum Rule, the derivative of with respect to is .
Step 3.10
Since is constant with respect to , the derivative of with respect to is .
Step 3.11
Differentiate using the Power Rule which states that is where .
Step 3.12
Multiply by .
Step 3.13
Since is constant with respect to , the derivative of with respect to is .
Step 3.14
Differentiate using the Power Rule which states that is where .
Step 3.15
Multiply by .
Step 4
Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
Step 4.2.1
Multiply by .
Step 4.2.2
Subtract from .
Step 4.2.3
Add and .
Step 4.2.4
Add and .
Step 4.3
Reorder terms.
Step 4.4
Simplify each term.
Step 4.4.1
Multiply by .
Step 4.4.2
Factor out of .
Step 4.4.2.1
Factor out of .
Step 4.4.2.2
Factor out of .
Step 4.4.2.3
Factor out of .
Step 4.4.3
Move to the left of .
Step 4.4.4
Multiply by .
Step 4.4.5
Factor out of .
Step 4.4.5.1
Factor out of .
Step 4.4.5.2
Factor out of .
Step 4.4.5.3
Factor out of .
Step 4.5
To write as a fraction with a common denominator, multiply by .
Step 4.6
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.6.1
Multiply by .
Step 4.6.2
Raise to the power of .
Step 4.6.3
Raise to the power of .
Step 4.6.4
Use the power rule to combine exponents.
Step 4.6.5
Add and .
Step 4.7
Combine the numerators over the common denominator.
Step 4.8
Simplify the numerator.
Step 4.8.1
Factor out of .
Step 4.8.1.1
Factor out of .
Step 4.8.1.2
Factor out of .
Step 4.8.1.3
Factor out of .
Step 4.8.2
Apply the distributive property.
Step 4.8.3
Rewrite using the commutative property of multiplication.
Step 4.8.4
Move to the left of .
Step 4.8.5
Simplify each term.
Step 4.8.5.1
Multiply by by adding the exponents.
Step 4.8.5.1.1
Move .
Step 4.8.5.1.2
Multiply by .
Step 4.8.5.1.2.1
Raise to the power of .
Step 4.8.5.1.2.2
Use the power rule to combine exponents.
Step 4.8.5.1.3
Add and .
Step 4.8.5.2
Rewrite as .
Step 4.8.6
Expand using the FOIL Method.
Step 4.8.6.1
Apply the distributive property.
Step 4.8.6.2
Apply the distributive property.
Step 4.8.6.3
Apply the distributive property.
Step 4.8.7
Simplify each term.
Step 4.8.7.1
Multiply by by adding the exponents.
Step 4.8.7.1.1
Move .
Step 4.8.7.1.2
Multiply by .
Step 4.8.7.1.2.1
Raise to the power of .
Step 4.8.7.1.2.2
Use the power rule to combine exponents.
Step 4.8.7.1.3
Add and .
Step 4.8.7.2
Multiply by .
Step 4.8.7.3
Rewrite as .
Step 4.8.7.4
Multiply by .
Step 4.8.8
Expand by multiplying each term in the first expression by each term in the second expression.
Step 4.8.9
Simplify each term.
Step 4.8.9.1
Multiply by by adding the exponents.
Step 4.8.9.1.1
Move .
Step 4.8.9.1.2
Multiply by .
Step 4.8.9.1.2.1
Raise to the power of .
Step 4.8.9.1.2.2
Use the power rule to combine exponents.
Step 4.8.9.1.3
Add and .
Step 4.8.9.2
Multiply by .
Step 4.8.9.3
Multiply by by adding the exponents.
Step 4.8.9.3.1
Move .
Step 4.8.9.3.2
Multiply by .
Step 4.8.9.3.2.1
Raise to the power of .
Step 4.8.9.3.2.2
Use the power rule to combine exponents.
Step 4.8.9.3.3
Add and .
Step 4.8.9.4
Multiply by .
Step 4.8.9.5
Multiply by by adding the exponents.
Step 4.8.9.5.1
Move .
Step 4.8.9.5.2
Multiply by .
Step 4.8.9.6
Multiply by .
Step 4.8.9.7
Multiply by .
Step 4.8.9.8
Multiply by .
Step 4.8.10
Combine the opposite terms in .
Step 4.8.10.1
Subtract from .
Step 4.8.10.2
Add and .
Step 4.8.10.3
Add and .
Step 4.8.10.4
Add and .
Step 4.8.11
Reorder terms.