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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Multiply by the reciprocal of the fraction to divide by .
Step 4
Multiply by .
Step 5
Differentiate using the Quotient Rule which states that is where and .
Step 6
Step 6.1
To apply the Chain Rule, set as .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Replace all occurrences of with .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Step 11.1
Move the negative in front of the fraction.
Step 11.2
Combine and .
Step 11.3
Move to the denominator using the negative exponent rule .
Step 11.4
Combine and .
Step 11.5
Combine and .
Step 12
By the Sum Rule, the derivative of with respect to is .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Step 15.1
Add and .
Step 15.2
Combine and .
Step 15.3
Combine and .
Step 16
Raise to the power of .
Step 17
Raise to the power of .
Step 18
Use the power rule to combine exponents.
Step 19
Add and .
Step 20
Cancel the common factor.
Step 21
Rewrite the expression.
Step 22
Multiply by .
Step 23
Combine.
Step 24
Apply the distributive property.
Step 25
Step 25.1
Cancel the common factor.
Step 25.2
Rewrite the expression.
Step 26
Step 26.1
Move .
Step 26.2
Use the power rule to combine exponents.
Step 26.3
Combine the numerators over the common denominator.
Step 26.4
Add and .
Step 26.5
Divide by .
Step 27
Simplify .
Step 28
Differentiate using the Product Rule which states that is where and .
Step 29
Step 29.1
To apply the Chain Rule, set as .
Step 29.2
Differentiate using the Power Rule which states that is where .
Step 29.3
Replace all occurrences of with .
Step 30
Step 30.1
By the Sum Rule, the derivative of with respect to is .
Step 30.2
Since is constant with respect to , the derivative of with respect to is .
Step 30.3
Differentiate using the Power Rule which states that is where .
Step 30.4
Multiply by .
Step 30.5
Since is constant with respect to , the derivative of with respect to is .
Step 30.6
Simplify the expression.
Step 30.6.1
Add and .
Step 30.6.2
Multiply by .
Step 31
Raise to the power of .
Step 32
Use the power rule to combine exponents.
Step 33
Add and .
Step 34
Differentiate using the Power Rule which states that is where .
Step 35
Step 35.1
Multiply by .
Step 35.2
Multiply by .
Step 36
Step 36.1
Move .
Step 36.2
Use the power rule to combine exponents.
Step 36.3
Combine the numerators over the common denominator.
Step 36.4
Add and .
Step 36.5
Divide by .
Step 37
Simplify .
Step 38
Step 38.1
Apply the product rule to .
Step 38.2
Apply the distributive property.
Step 38.3
Apply the distributive property.
Step 38.4
Apply the distributive property.
Step 38.5
Simplify the numerator.
Step 38.5.1
Combine exponents.
Step 38.5.1.1
Multiply by .
Step 38.5.1.2
Multiply by .
Step 38.5.1.3
Multiply by by adding the exponents.
Step 38.5.1.3.1
Move .
Step 38.5.1.3.2
Use the power rule to combine exponents.
Step 38.5.1.3.3
Add and .
Step 38.5.1.4
Multiply by .
Step 38.5.1.5
Multiply by .
Step 38.5.2
Simplify each term.
Step 38.5.2.1
Rewrite as .
Step 38.5.2.2
Expand using the FOIL Method.
Step 38.5.2.2.1
Apply the distributive property.
Step 38.5.2.2.2
Apply the distributive property.
Step 38.5.2.2.3
Apply the distributive property.
Step 38.5.2.3
Simplify and combine like terms.
Step 38.5.2.3.1
Simplify each term.
Step 38.5.2.3.1.1
Rewrite using the commutative property of multiplication.
Step 38.5.2.3.1.2
Multiply by by adding the exponents.
Step 38.5.2.3.1.2.1
Move .
Step 38.5.2.3.1.2.2
Use the power rule to combine exponents.
Step 38.5.2.3.1.2.3
Add and .
Step 38.5.2.3.1.3
Multiply by .
Step 38.5.2.3.1.4
Multiply by .
Step 38.5.2.3.1.5
Multiply by .
Step 38.5.2.3.1.6
Multiply by .
Step 38.5.2.3.2
Subtract from .
Step 38.5.2.4
Apply the distributive property.
Step 38.5.2.5
Simplify.
Step 38.5.2.5.1
Rewrite using the commutative property of multiplication.
Step 38.5.2.5.2
Rewrite using the commutative property of multiplication.
Step 38.5.2.5.3
Multiply by .
Step 38.5.2.6
Simplify each term.
Step 38.5.2.6.1
Multiply by by adding the exponents.
Step 38.5.2.6.1.1
Move .
Step 38.5.2.6.1.2
Use the power rule to combine exponents.
Step 38.5.2.6.1.3
Add and .
Step 38.5.2.6.2
Multiply by by adding the exponents.
Step 38.5.2.6.2.1
Move .
Step 38.5.2.6.2.2
Use the power rule to combine exponents.
Step 38.5.2.6.2.3
Add and .
Step 38.5.2.7
Simplify each term.
Step 38.5.2.7.1
Rewrite as .
Step 38.5.2.7.2
Expand using the FOIL Method.
Step 38.5.2.7.2.1
Apply the distributive property.
Step 38.5.2.7.2.2
Apply the distributive property.
Step 38.5.2.7.2.3
Apply the distributive property.
Step 38.5.2.7.3
Simplify and combine like terms.
Step 38.5.2.7.3.1
Simplify each term.
Step 38.5.2.7.3.1.1
Rewrite using the commutative property of multiplication.
Step 38.5.2.7.3.1.2
Multiply by by adding the exponents.
Step 38.5.2.7.3.1.2.1
Move .
Step 38.5.2.7.3.1.2.2
Use the power rule to combine exponents.
Step 38.5.2.7.3.1.2.3
Add and .
Step 38.5.2.7.3.1.3
Multiply by .
Step 38.5.2.7.3.1.4
Multiply by .
Step 38.5.2.7.3.1.5
Multiply by .
Step 38.5.2.7.3.1.6
Multiply by .
Step 38.5.2.7.3.2
Subtract from .
Step 38.5.2.7.4
Apply the distributive property.
Step 38.5.2.7.5
Simplify.
Step 38.5.2.7.5.1
Multiply by .
Step 38.5.2.7.5.2
Multiply by .
Step 38.5.2.7.5.3
Multiply by .
Step 38.5.2.8
Subtract from .
Step 38.5.2.9
Add and .
Step 38.5.2.10
Expand by multiplying each term in the first expression by each term in the second expression.
Step 38.5.2.11
Simplify each term.
Step 38.5.2.11.1
Rewrite using the commutative property of multiplication.
Step 38.5.2.11.2
Multiply by by adding the exponents.
Step 38.5.2.11.2.1
Move .
Step 38.5.2.11.2.2
Use the power rule to combine exponents.
Step 38.5.2.11.2.3
Add and .
Step 38.5.2.11.3
Rewrite using the commutative property of multiplication.
Step 38.5.2.11.4
Multiply by by adding the exponents.
Step 38.5.2.11.4.1
Move .
Step 38.5.2.11.4.2
Use the power rule to combine exponents.
Step 38.5.2.11.4.3
Add and .
Step 38.5.2.11.5
Move to the left of .
Step 38.5.2.11.6
Rewrite as .
Step 38.5.2.11.7
Multiply by .
Step 38.5.2.11.8
Multiply by .
Step 38.5.2.11.9
Multiply by .
Step 38.5.3
Combine the opposite terms in .
Step 38.5.3.1
Subtract from .
Step 38.5.3.2
Add and .
Step 38.5.4
Subtract from .
Step 38.5.5
Add and .
Step 38.5.6
Reorder terms.
Step 38.6
Combine terms.
Step 38.6.1
Multiply the exponents in .
Step 38.6.1.1
Apply the power rule and multiply exponents, .
Step 38.6.1.2
Multiply by .
Step 38.6.2
Cancel the common factor of and .
Step 38.6.2.1
Factor out of .
Step 38.6.2.2
Cancel the common factors.
Step 38.6.2.2.1
Factor out of .
Step 38.6.2.2.2
Cancel the common factor.
Step 38.6.2.2.3
Rewrite the expression.
Step 38.6.3
Cancel the common factors.
Step 38.6.3.1
Factor out of .
Step 38.6.3.2
Cancel the common factor.
Step 38.6.3.3
Rewrite the expression.
Step 38.7
Reorder terms.
Step 38.8
Factor out of .
Step 38.9
Factor out of .
Step 38.10
Factor out of .
Step 38.11
Factor out of .
Step 38.12
Factor out of .
Step 38.13
Factor out of .
Step 38.14
Factor out of .
Step 38.15
Rewrite as .
Step 38.16
Factor out of .
Step 38.17
Rewrite as .
Step 38.18
Move the negative in front of the fraction.