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Calculus Examples
Step 1
Rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Add and .
Step 4.6
By the Sum Rule, the derivative of with respect to is .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Since is constant with respect to , the derivative of with respect to is .
Step 4.9
Simplify the expression.
Step 4.9.1
Add and .
Step 4.9.2
Move to the left of .
Step 5
Step 5.1
Rewrite the expression using the negative exponent rule .
Step 5.2
Apply the product rule to .
Step 5.3
Apply the distributive property.
Step 5.4
Apply the distributive property.
Step 5.5
Combine terms.
Step 5.5.1
Raise to the power of .
Step 5.5.2
Use the power rule to combine exponents.
Step 5.5.3
Add and .
Step 5.5.4
Raise to the power of .
Step 5.5.5
Raise to the power of .
Step 5.5.6
Use the power rule to combine exponents.
Step 5.5.7
Add and .
Step 5.5.8
Multiply by .
Step 5.6
Reorder the factors of .
Step 5.7
Simplify each term.
Step 5.7.1
Expand using the FOIL Method.
Step 5.7.1.1
Apply the distributive property.
Step 5.7.1.2
Apply the distributive property.
Step 5.7.1.3
Apply the distributive property.
Step 5.7.2
Simplify each term.
Step 5.7.2.1
Rewrite using the commutative property of multiplication.
Step 5.7.2.2
Multiply by by adding the exponents.
Step 5.7.2.2.1
Move .
Step 5.7.2.2.2
Multiply by .
Step 5.7.2.2.2.1
Raise to the power of .
Step 5.7.2.2.2.2
Use the power rule to combine exponents.
Step 5.7.2.2.3
Add and .
Step 5.7.2.3
Multiply by .
Step 5.7.2.4
Multiply by .
Step 5.7.2.5
Multiply by .
Step 5.8
Combine the opposite terms in .
Step 5.8.1
Add and .
Step 5.8.2
Add and .
Step 5.9
Add and .
Step 5.10
Add and .
Step 5.11
Apply the distributive property.
Step 5.12
Simplify.
Step 5.12.1
Multiply by .
Step 5.12.2
Multiply by .
Step 5.12.3
Multiply by .
Step 5.13
Simplify the denominator.
Step 5.13.1
Rewrite as .
Step 5.13.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.13.3
Apply the product rule to .
Step 5.14
Multiply by .
Step 5.15
Factor out of .
Step 5.16
Factor out of .
Step 5.17
Factor out of .
Step 5.18
Rewrite as .
Step 5.19
Factor out of .
Step 5.20
Rewrite as .
Step 5.21
Move the negative in front of the fraction.