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Calculus Examples
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
Multiply the exponents in .
Step 3.1.1
Apply the power rule and multiply exponents, .
Step 3.1.2
Multiply by .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Move to the left of .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
Step 5.1
Multiply by .
Step 5.2
By the Sum Rule, the derivative of with respect to is .
Step 5.3
Since is constant with respect to , the derivative of with respect to is .
Step 5.4
Add and .
Step 5.5
Since is constant with respect to , the derivative of with respect to is .
Step 5.6
Simplify the expression.
Step 5.6.1
Move to the left of .
Step 5.6.2
Multiply by .
Step 5.7
Differentiate using the Power Rule which states that is where .
Step 5.8
Combine fractions.
Step 5.8.1
Multiply by .
Step 5.8.2
Combine and .
Step 6
Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Simplify the numerator.
Step 6.3.1
Simplify each term.
Step 6.3.1.1
Rewrite as .
Step 6.3.1.2
Expand using the FOIL Method.
Step 6.3.1.2.1
Apply the distributive property.
Step 6.3.1.2.2
Apply the distributive property.
Step 6.3.1.2.3
Apply the distributive property.
Step 6.3.1.3
Simplify and combine like terms.
Step 6.3.1.3.1
Simplify each term.
Step 6.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.2
Multiply by by adding the exponents.
Step 6.3.1.3.1.2.1
Move .
Step 6.3.1.3.1.2.2
Multiply by .
Step 6.3.1.3.1.3
Multiply by .
Step 6.3.1.3.1.4
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.5
Multiply by .
Step 6.3.1.3.1.6
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.7
Multiply by .
Step 6.3.1.3.1.8
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.9
Multiply by by adding the exponents.
Step 6.3.1.3.1.9.1
Move .
Step 6.3.1.3.1.9.2
Multiply by .
Step 6.3.1.3.1.10
Multiply by .
Step 6.3.1.3.2
Add and .
Step 6.3.1.3.2.1
Move .
Step 6.3.1.3.2.2
Add and .
Step 6.3.1.4
Apply the distributive property.
Step 6.3.1.5
Simplify.
Step 6.3.1.5.1
Multiply by .
Step 6.3.1.5.2
Multiply by .
Step 6.3.1.5.3
Multiply by .
Step 6.3.1.6
Apply the distributive property.
Step 6.3.1.7
Simplify.
Step 6.3.1.7.1
Multiply by by adding the exponents.
Step 6.3.1.7.1.1
Move .
Step 6.3.1.7.1.2
Multiply by .
Step 6.3.1.7.2
Multiply by by adding the exponents.
Step 6.3.1.7.2.1
Move .
Step 6.3.1.7.2.2
Multiply by .
Step 6.3.1.7.2.2.1
Raise to the power of .
Step 6.3.1.7.2.2.2
Use the power rule to combine exponents.
Step 6.3.1.7.2.3
Add and .
Step 6.3.1.8
Apply the distributive property.
Step 6.3.1.9
Simplify.
Step 6.3.1.9.1
Multiply by .
Step 6.3.1.9.2
Multiply by .
Step 6.3.1.9.3
Multiply by .
Step 6.3.1.10
Remove parentheses.
Step 6.3.1.11
Rewrite using the commutative property of multiplication.
Step 6.3.1.12
Multiply by .
Step 6.3.1.13
Multiply by .
Step 6.3.1.14
Multiply by by adding the exponents.
Step 6.3.1.14.1
Move .
Step 6.3.1.14.2
Multiply by .
Step 6.3.1.14.2.1
Raise to the power of .
Step 6.3.1.14.2.2
Use the power rule to combine exponents.
Step 6.3.1.14.3
Add and .
Step 6.3.1.15
Multiply by .
Step 6.3.1.16
Multiply by .
Step 6.3.2
Combine the opposite terms in .
Step 6.3.2.1
Subtract from .
Step 6.3.2.2
Add and .
Step 6.3.3
Subtract from .
Step 6.3.3.1
Move .
Step 6.3.3.2
Subtract from .
Step 6.4
Reorder terms.
Step 6.5
Factor out of .
Step 6.5.1
Factor out of .
Step 6.5.2
Factor out of .
Step 6.5.3
Factor out of .
Step 6.6
Cancel the common factor of and .
Step 6.6.1
Factor out of .
Step 6.6.2
Cancel the common factors.
Step 6.6.2.1
Factor out of .
Step 6.6.2.2
Cancel the common factor.
Step 6.6.2.3
Rewrite the expression.