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Calculus Examples
Step 1
Step 1.1
Combine and .
Step 1.2
Combine fractions.
Step 1.2.1
Combine and .
Step 1.2.2
Move to the left of .
Step 1.3
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
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 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Multiply by .
Step 4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.6
Simplify the expression.
Step 4.6.1
Add and .
Step 4.6.2
Multiply by .
Step 5
Step 5.1
Move .
Step 5.2
Use the power rule to combine exponents.
Step 5.3
Add and .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
Move to the left of .
Step 8
Step 8.1
Apply the distributive property.
Step 8.2
Combine and .
Step 8.3
Combine and .
Step 8.4
Multiply by .
Step 8.5
Combine and .
Step 8.6
Cancel the common factor of and .
Step 8.6.1
Factor out of .
Step 8.6.2
Cancel the common factors.
Step 8.6.2.1
Factor out of .
Step 8.6.2.2
Cancel the common factor.
Step 8.6.2.3
Rewrite the expression.
Step 8.6.2.4
Divide by .
Step 8.7
Combine and .
Step 8.8
Multiply by .
Step 8.9
Combine and .
Step 8.10
Combine and .
Step 8.11
Move to the left of .
Step 8.12
Cancel the common factor of and .
Step 8.12.1
Factor out of .
Step 8.12.2
Cancel the common factors.
Step 8.12.2.1
Factor out of .
Step 8.12.2.2
Cancel the common factor.
Step 8.12.2.3
Rewrite the expression.
Step 8.12.2.4
Divide by .
Step 8.13
Factor out of .
Step 8.13.1
Factor out of .
Step 8.13.2
Factor out of .
Step 8.13.3
Factor out of .
Step 8.14
Add and .
Step 8.15
Rewrite as .
Step 8.16
Expand using the FOIL Method.
Step 8.16.1
Apply the distributive property.
Step 8.16.2
Apply the distributive property.
Step 8.16.3
Apply the distributive property.
Step 8.17
Simplify and combine like terms.
Step 8.17.1
Simplify each term.
Step 8.17.1.1
Rewrite using the commutative property of multiplication.
Step 8.17.1.2
Multiply by by adding the exponents.
Step 8.17.1.2.1
Move .
Step 8.17.1.2.2
Use the power rule to combine exponents.
Step 8.17.1.2.3
Add and .
Step 8.17.1.3
Multiply by .
Step 8.17.1.4
Multiply by .
Step 8.17.1.5
Multiply by .
Step 8.17.1.6
Multiply by .
Step 8.17.2
Subtract from .
Step 8.18
Apply the distributive property.
Step 8.19
Simplify.
Step 8.19.1
Rewrite using the commutative property of multiplication.
Step 8.19.2
Rewrite using the commutative property of multiplication.
Step 8.19.3
Multiply by .
Step 8.20
Simplify each term.
Step 8.20.1
Multiply by by adding the exponents.
Step 8.20.1.1
Move .
Step 8.20.1.2
Use the power rule to combine exponents.
Step 8.20.1.3
Add and .
Step 8.20.2
Multiply by .
Step 8.20.3
Multiply by by adding the exponents.
Step 8.20.3.1
Move .
Step 8.20.3.2
Use the power rule to combine exponents.
Step 8.20.3.3
Add and .
Step 8.20.4
Multiply by .
Step 8.21
Expand by multiplying each term in the first expression by each term in the second expression.
Step 8.22
Simplify each term.
Step 8.22.1
Rewrite using the commutative property of multiplication.
Step 8.22.2
Multiply by by adding the exponents.
Step 8.22.2.1
Move .
Step 8.22.2.2
Use the power rule to combine exponents.
Step 8.22.2.3
Add and .
Step 8.22.3
Multiply by .
Step 8.22.4
Multiply by .
Step 8.22.5
Rewrite using the commutative property of multiplication.
Step 8.22.6
Multiply by by adding the exponents.
Step 8.22.6.1
Move .
Step 8.22.6.2
Use the power rule to combine exponents.
Step 8.22.6.3
Add and .
Step 8.22.7
Multiply by .
Step 8.22.8
Multiply by .
Step 8.22.9
Rewrite using the commutative property of multiplication.
Step 8.22.10
Multiply by by adding the exponents.
Step 8.22.10.1
Move .
Step 8.22.10.2
Use the power rule to combine exponents.
Step 8.22.10.3
Add and .
Step 8.22.11
Multiply by .
Step 8.22.12
Multiply by .
Step 8.23
Subtract from .
Step 8.24
Add and .