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Calculus Examples
Step 1
Differentiate using the Product 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 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Multiply by .
Step 2.6
Since is constant with respect to , the derivative of with respect to is .
Step 2.7
Differentiate using the Power Rule which states that is where .
Step 2.8
Multiply by .
Step 2.9
By the Sum Rule, the derivative of with respect to is .
Step 2.10
Differentiate using the Power Rule which states that is where .
Step 2.11
Since is constant with respect to , the derivative of with respect to is .
Step 2.12
Differentiate using the Power Rule which states that is where .
Step 2.13
Multiply by .
Step 2.14
Since is constant with respect to , the derivative of with respect to is .
Step 2.15
Add and .
Step 3
Step 3.1
Factor out of .
Step 3.1.1
Factor out of .
Step 3.1.2
Factor out of .
Step 3.1.3
Factor out of .
Step 3.2
Multiply by .
Step 3.3
Reorder terms.
Step 3.4
Simplify each term.
Step 3.4.1
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3.4.2
Simplify each term.
Step 3.4.2.1
Multiply by by adding the exponents.
Step 3.4.2.1.1
Move .
Step 3.4.2.1.2
Use the power rule to combine exponents.
Step 3.4.2.1.3
Add and .
Step 3.4.2.2
Rewrite using the commutative property of multiplication.
Step 3.4.2.3
Multiply by by adding the exponents.
Step 3.4.2.3.1
Move .
Step 3.4.2.3.2
Multiply by .
Step 3.4.2.3.2.1
Raise to the power of .
Step 3.4.2.3.2.2
Use the power rule to combine exponents.
Step 3.4.2.3.3
Add and .
Step 3.4.2.4
Multiply by .
Step 3.4.2.5
Multiply by .
Step 3.4.2.6
Multiply by by adding the exponents.
Step 3.4.2.6.1
Move .
Step 3.4.2.6.2
Multiply by .
Step 3.4.2.6.2.1
Raise to the power of .
Step 3.4.2.6.2.2
Use the power rule to combine exponents.
Step 3.4.2.6.3
Add and .
Step 3.4.2.7
Rewrite using the commutative property of multiplication.
Step 3.4.2.8
Multiply by by adding the exponents.
Step 3.4.2.8.1
Move .
Step 3.4.2.8.2
Multiply by .
Step 3.4.2.9
Multiply by .
Step 3.4.2.10
Multiply by .
Step 3.4.2.11
Multiply by .
Step 3.4.2.12
Multiply by .
Step 3.4.3
Subtract from .
Step 3.4.4
Add and .
Step 3.4.5
Subtract from .
Step 3.4.6
Add and .
Step 3.4.7
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3.4.8
Simplify each term.
Step 3.4.8.1
Multiply by by adding the exponents.
Step 3.4.8.1.1
Move .
Step 3.4.8.1.2
Multiply by .
Step 3.4.8.1.2.1
Raise to the power of .
Step 3.4.8.1.2.2
Use the power rule to combine exponents.
Step 3.4.8.1.3
Add and .
Step 3.4.8.2
Rewrite using the commutative property of multiplication.
Step 3.4.8.3
Multiply by by adding the exponents.
Step 3.4.8.3.1
Move .
Step 3.4.8.3.2
Multiply by .
Step 3.4.8.3.2.1
Raise to the power of .
Step 3.4.8.3.2.2
Use the power rule to combine exponents.
Step 3.4.8.3.3
Add and .
Step 3.4.8.4
Multiply by .
Step 3.4.8.5
Rewrite using the commutative property of multiplication.
Step 3.4.8.6
Multiply by by adding the exponents.
Step 3.4.8.6.1
Move .
Step 3.4.8.6.2
Multiply by .
Step 3.4.8.7
Multiply by .
Step 3.4.8.8
Multiply by .
Step 3.4.8.9
Multiply by .
Step 3.4.9
Subtract from .
Step 3.4.10
Add and .
Step 3.5
Add and .
Step 3.6
Subtract from .
Step 3.7
Add and .
Step 3.8
Add and .