Calculus Examples

Find the 2nd Derivative f(x)=(3x^3+7)^7
Step 1
Find the first derivative.
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Step 1.1
Differentiate using the chain rule, which states that is where and .
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Step 1.1.1
To apply the Chain Rule, set as .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3
Replace all occurrences of with .
Step 1.2
Differentiate.
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Step 1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 1.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.2.3
Differentiate using the Power Rule which states that is where .
Step 1.2.4
Multiply by .
Step 1.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 1.2.6
Simplify the expression.
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Step 1.2.6.1
Add and .
Step 1.2.6.2
Multiply by .
Step 1.2.6.3
Reorder the factors of .
Step 2
Find the second derivative.
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the Product Rule which states that is where and .
Step 2.3
Differentiate using the chain rule, which states that is where and .
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Step 2.3.1
To apply the Chain Rule, set as .
Step 2.3.2
Differentiate using the Power Rule which states that is where .
Step 2.3.3
Replace all occurrences of with .
Step 2.4
Differentiate.
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Step 2.4.1
By the Sum Rule, the derivative of with respect to is .
Step 2.4.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.4.3
Differentiate using the Power Rule which states that is where .
Step 2.4.4
Multiply by .
Step 2.4.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.4.6
Simplify the expression.
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Step 2.4.6.1
Add and .
Step 2.4.6.2
Multiply by .
Step 2.5
Multiply by by adding the exponents.
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Step 2.5.1
Move .
Step 2.5.2
Use the power rule to combine exponents.
Step 2.5.3
Add and .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Move to the left of .
Step 2.8
Simplify.
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Step 2.8.1
Apply the distributive property.
Step 2.8.2
Multiply by .
Step 2.8.3
Multiply by .
Step 2.8.4
Factor out of .
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Step 2.8.4.1
Factor out of .
Step 2.8.4.2
Factor out of .
Step 2.8.4.3
Factor out of .
Step 2.8.5
Add and .
Step 3
Find the third derivative.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Product Rule which states that is where and .
Step 3.3
Differentiate.
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Step 3.3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.3
Differentiate using the Power Rule which states that is where .
Step 3.3.4
Multiply by .
Step 3.3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.6
Add and .
Step 3.4
Raise to the power of .
Step 3.5
Use the power rule to combine exponents.
Step 3.6
Simplify the expression.
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Step 3.6.1
Add and .
Step 3.6.2
Move to the left of .
Step 3.7
Differentiate using the Product Rule which states that is where and .
Step 3.8
Differentiate using the chain rule, which states that is where and .
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Step 3.8.1
To apply the Chain Rule, set as .
Step 3.8.2
Differentiate using the Power Rule which states that is where .
Step 3.8.3
Replace all occurrences of with .
Step 3.9
Differentiate.
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Step 3.9.1
By the Sum Rule, the derivative of with respect to is .
Step 3.9.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.9.3
Differentiate using the Power Rule which states that is where .
Step 3.9.4
Multiply by .
Step 3.9.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.9.6
Simplify the expression.
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Step 3.9.6.1
Add and .
Step 3.9.6.2
Multiply by .
Step 3.10
Raise to the power of .
Step 3.11
Use the power rule to combine exponents.
Step 3.12
Add and .
Step 3.13
Differentiate using the Power Rule which states that is where .
Step 3.14
Multiply by .
Step 4
Find the fourth derivative.
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Step 4.1
Differentiate.
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Step 4.1.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.1.2
By the Sum Rule, the derivative of with respect to is .
Step 4.1.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Differentiate using the Product Rule which states that is where and .
Step 4.3
Differentiate using the chain rule, which states that is where and .
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Step 4.3.1
To apply the Chain Rule, set as .
Step 4.3.2
Differentiate using the Power Rule which states that is where .
Step 4.3.3
Replace all occurrences of with .
Step 4.4
Differentiate.
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Step 4.4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.4.3
Differentiate using the Power Rule which states that is where .
Step 4.4.4
Multiply by .
Step 4.4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.4.6
Simplify the expression.
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Step 4.4.6.1
Add and .
Step 4.4.6.2
Multiply by .
Step 4.5
Multiply by by adding the exponents.
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Step 4.5.1
Move .
Step 4.5.2
Use the power rule to combine exponents.
Step 4.5.3
Add and .
Step 4.6
Differentiate using the Power Rule.
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Step 4.6.1
Differentiate using the Power Rule which states that is where .
Step 4.6.2
Move to the left of .
Step 4.7
Differentiate using the Product Rule which states that is where and .
Step 4.8
Differentiate.
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Step 4.8.1
By the Sum Rule, the derivative of with respect to is .
Step 4.8.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.9
Differentiate using the Product Rule which states that is where and .
Step 4.10
Differentiate using the chain rule, which states that is where and .
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Step 4.10.1
To apply the Chain Rule, set as .
Step 4.10.2
Differentiate using the Power Rule which states that is where .
Step 4.10.3
Replace all occurrences of with .
Step 4.11
Differentiate.
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Step 4.11.1
By the Sum Rule, the derivative of with respect to is .
Step 4.11.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.11.3
Differentiate using the Power Rule which states that is where .
Step 4.11.4
Multiply by .
Step 4.11.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.11.6
Simplify the expression.
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Step 4.11.6.1
Add and .
Step 4.11.6.2
Multiply by .
Step 4.12
Multiply by by adding the exponents.
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Step 4.12.1
Move .
Step 4.12.2
Use the power rule to combine exponents.
Step 4.12.3
Add and .
Step 4.13
Differentiate using the Power Rule.
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Step 4.13.1
Differentiate using the Power Rule which states that is where .
Step 4.13.2
Move to the left of .
Step 4.14
Differentiate using the chain rule, which states that is where and .
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Step 4.14.1
To apply the Chain Rule, set as .
Step 4.14.2
Differentiate using the Power Rule which states that is where .
Step 4.14.3
Replace all occurrences of with .
Step 4.15
Differentiate.
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Step 4.15.1
By the Sum Rule, the derivative of with respect to is .
Step 4.15.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.15.3
Differentiate using the Power Rule which states that is where .
Step 4.15.4
Multiply by .
Step 4.15.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.15.6
Simplify the expression.
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Step 4.15.6.1
Add and .
Step 4.15.6.2
Multiply by .
Step 4.15.7
By the Sum Rule, the derivative of with respect to is .
Step 4.15.8
Since is constant with respect to , the derivative of with respect to is .
Step 4.15.9
Differentiate using the Power Rule which states that is where .
Step 4.15.10
Multiply by .
Step 4.15.11
Since is constant with respect to , the derivative of with respect to is .
Step 4.15.12
Simplify the expression.
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Step 4.15.12.1
Add and .
Step 4.15.12.2
Move to the left of .
Step 4.16
Simplify.
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Step 4.16.1
Apply the distributive property.
Step 4.16.2
Apply the distributive property.
Step 4.16.3
Apply the distributive property.
Step 4.16.4
Apply the distributive property.
Step 4.16.5
Apply the distributive property.
Step 4.16.6
Multiply by .
Step 4.16.7
Multiply by .
Step 4.16.8
Multiply by .
Step 4.16.9
Multiply by .
Step 4.16.10
Multiply by .
Step 4.16.11
Multiply by .
Step 4.16.12
Add and .
Step 4.16.13
Multiply by .
Step 4.16.14
Multiply by by adding the exponents.
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Step 4.16.14.1
Move .
Step 4.16.14.2
Use the power rule to combine exponents.
Step 4.16.14.3
Add and .
Step 4.16.15
Multiply by .
Step 4.16.16
Multiply by .
Step 4.16.17
Add and .
Step 4.16.18
Add and .
Step 4.16.19
Factor out of .
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Step 4.16.19.1
Factor out of .
Step 4.16.19.2
Factor out of .
Step 4.16.19.3
Factor out of .
Step 4.16.19.4
Factor out of .
Step 4.16.19.5
Factor out of .
Step 4.16.20
Simplify each term.
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Step 4.16.20.1
Use the Binomial Theorem.
Step 4.16.20.2
Simplify each term.
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Step 4.16.20.2.1
Apply the product rule to .
Step 4.16.20.2.2
Raise to the power of .
Step 4.16.20.2.3
Multiply the exponents in .
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Step 4.16.20.2.3.1
Apply the power rule and multiply exponents, .
Step 4.16.20.2.3.2
Multiply by .
Step 4.16.20.2.4
Apply the product rule to .
Step 4.16.20.2.5
Raise to the power of .
Step 4.16.20.2.6
Multiply the exponents in .
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Step 4.16.20.2.6.1
Apply the power rule and multiply exponents, .
Step 4.16.20.2.6.2
Multiply by .
Step 4.16.20.2.7
Multiply by .
Step 4.16.20.2.8
Multiply by .
Step 4.16.20.2.9
Apply the product rule to .
Step 4.16.20.2.10
Raise to the power of .
Step 4.16.20.2.11
Multiply the exponents in .
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Step 4.16.20.2.11.1
Apply the power rule and multiply exponents, .
Step 4.16.20.2.11.2
Multiply by .
Step 4.16.20.2.12
Multiply by .
Step 4.16.20.2.13
Raise to the power of .
Step 4.16.20.2.14
Multiply by .
Step 4.16.20.2.15
Multiply by .
Step 4.16.20.2.16
Raise to the power of .
Step 4.16.20.2.17
Multiply by .
Step 4.16.20.2.18
Raise to the power of .
Step 4.16.20.3
Apply the distributive property.
Step 4.16.20.4
Simplify.
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Step 4.16.20.4.1
Rewrite using the commutative property of multiplication.
Step 4.16.20.4.2
Rewrite using the commutative property of multiplication.
Step 4.16.20.4.3
Rewrite using the commutative property of multiplication.
Step 4.16.20.4.4
Rewrite using the commutative property of multiplication.
Step 4.16.20.4.5
Multiply by .
Step 4.16.20.5
Simplify each term.
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Step 4.16.20.5.1
Multiply by by adding the exponents.
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Step 4.16.20.5.1.1
Move .
Step 4.16.20.5.1.2
Use the power rule to combine exponents.
Step 4.16.20.5.1.3
Add and .
Step 4.16.20.5.2
Multiply by .
Step 4.16.20.5.3
Multiply by by adding the exponents.
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Step 4.16.20.5.3.1
Move .
Step 4.16.20.5.3.2
Use the power rule to combine exponents.
Step 4.16.20.5.3.3
Add and .
Step 4.16.20.5.4
Multiply by .
Step 4.16.20.5.5
Multiply by by adding the exponents.
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Step 4.16.20.5.5.1
Move .
Step 4.16.20.5.5.2
Use the power rule to combine exponents.
Step 4.16.20.5.5.3
Add and .
Step 4.16.20.5.6
Multiply by .
Step 4.16.20.5.7
Multiply by by adding the exponents.
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Step 4.16.20.5.7.1
Move .
Step 4.16.20.5.7.2
Use the power rule to combine exponents.
Step 4.16.20.5.7.3
Add and .
Step 4.16.20.5.8
Multiply by .
Step 4.16.20.6
Use the Binomial Theorem.
Step 4.16.20.7
Simplify each term.
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Step 4.16.20.7.1
Apply the product rule to .
Step 4.16.20.7.2
Raise to the power of .
Step 4.16.20.7.3
Multiply the exponents in .
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Step 4.16.20.7.3.1
Apply the power rule and multiply exponents, .
Step 4.16.20.7.3.2
Multiply by .
Step 4.16.20.7.4
Apply the product rule to .
Step 4.16.20.7.5
Raise to the power of .
Step 4.16.20.7.6
Multiply the exponents in .
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Step 4.16.20.7.6.1
Apply the power rule and multiply exponents, .
Step 4.16.20.7.6.2
Multiply by .
Step 4.16.20.7.7
Multiply by .
Step 4.16.20.7.8
Multiply by .
Step 4.16.20.7.9
Apply the product rule to .
Step 4.16.20.7.10
Raise to the power of .
Step 4.16.20.7.11
Multiply the exponents in .
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Step 4.16.20.7.11.1
Apply the power rule and multiply exponents, .
Step 4.16.20.7.11.2
Multiply by .
Step 4.16.20.7.12
Multiply by .
Step 4.16.20.7.13
Raise to the power of .
Step 4.16.20.7.14
Multiply by .
Step 4.16.20.7.15
Apply the product rule to .
Step 4.16.20.7.16
Raise to the power of .
Step 4.16.20.7.17
Multiply the exponents in .
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Step 4.16.20.7.17.1
Apply the power rule and multiply exponents, .
Step 4.16.20.7.17.2
Multiply by .
Step 4.16.20.7.18
Multiply by .
Step 4.16.20.7.19
Raise to the power of .
Step 4.16.20.7.20
Multiply by .
Step 4.16.20.7.21
Multiply by .
Step 4.16.20.7.22
Raise to the power of .
Step 4.16.20.7.23
Multiply by .
Step 4.16.20.7.24
Raise to the power of .
Step 4.16.20.8
Apply the distributive property.
Step 4.16.20.9
Simplify.
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Step 4.16.20.9.1
Multiply by .
Step 4.16.20.9.2
Multiply by .
Step 4.16.20.9.3
Multiply by .
Step 4.16.20.9.4
Multiply by .
Step 4.16.20.9.5
Multiply by .
Step 4.16.20.9.6
Multiply by .
Step 4.16.20.10
Apply the distributive property.
Step 4.16.20.11
Simplify.
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Step 4.16.20.11.1
Multiply by by adding the exponents.
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Step 4.16.20.11.1.1
Move .
Step 4.16.20.11.1.2
Use the power rule to combine exponents.
Step 4.16.20.11.1.3
Add and .
Step 4.16.20.11.2
Multiply by by adding the exponents.
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Step 4.16.20.11.2.1
Move .
Step 4.16.20.11.2.2
Use the power rule to combine exponents.
Step 4.16.20.11.2.3
Add and .
Step 4.16.20.11.3
Multiply by by adding the exponents.
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Step 4.16.20.11.3.1
Move .
Step 4.16.20.11.3.2
Use the power rule to combine exponents.
Step 4.16.20.11.3.3
Add and .
Step 4.16.20.11.4
Multiply by by adding the exponents.
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Step 4.16.20.11.4.1
Move .
Step 4.16.20.11.4.2
Use the power rule to combine exponents.
Step 4.16.20.11.4.3
Add and .
Step 4.16.20.11.5
Multiply by by adding the exponents.
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Step 4.16.20.11.5.1
Move .
Step 4.16.20.11.5.2
Use the power rule to combine exponents.
Step 4.16.20.11.5.3
Add and .
Step 4.16.20.12
Simplify each term.
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Step 4.16.20.12.1
Use the Binomial Theorem.
Step 4.16.20.12.2
Simplify each term.
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Step 4.16.20.12.2.1
Apply the product rule to .
Step 4.16.20.12.2.2
Raise to the power of .
Step 4.16.20.12.2.3
Multiply the exponents in .
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Step 4.16.20.12.2.3.1
Apply the power rule and multiply exponents, .
Step 4.16.20.12.2.3.2
Multiply by .
Step 4.16.20.12.2.4
Apply the product rule to .
Step 4.16.20.12.2.5
Multiply by by adding the exponents.
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Step 4.16.20.12.2.5.1
Move .
Step 4.16.20.12.2.5.2
Multiply by .
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Step 4.16.20.12.2.5.2.1
Raise to the power of .
Step 4.16.20.12.2.5.2.2
Use the power rule to combine exponents.
Step 4.16.20.12.2.5.3
Add and .
Step 4.16.20.12.2.6
Raise to the power of .
Step 4.16.20.12.2.7
Multiply the exponents in .
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Step 4.16.20.12.2.7.1
Apply the power rule and multiply exponents, .
Step 4.16.20.12.2.7.2
Multiply by .
Step 4.16.20.12.2.8
Multiply by .
Step 4.16.20.12.2.9
Multiply by .
Step 4.16.20.12.2.10
Raise to the power of .
Step 4.16.20.12.2.11
Multiply by .
Step 4.16.20.12.2.12
Raise to the power of .
Step 4.16.20.12.3
Apply the distributive property.
Step 4.16.20.12.4
Simplify.
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Step 4.16.20.12.4.1
Rewrite using the commutative property of multiplication.
Step 4.16.20.12.4.2
Rewrite using the commutative property of multiplication.
Step 4.16.20.12.4.3
Rewrite using the commutative property of multiplication.
Step 4.16.20.12.4.4
Multiply by .
Step 4.16.20.12.5
Simplify each term.
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Step 4.16.20.12.5.1
Multiply by by adding the exponents.
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Step 4.16.20.12.5.1.1
Move .
Step 4.16.20.12.5.1.2
Use the power rule to combine exponents.
Step 4.16.20.12.5.1.3
Add and .
Step 4.16.20.12.5.2
Multiply by .
Step 4.16.20.12.5.3
Multiply by by adding the exponents.
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Step 4.16.20.12.5.3.1
Move .
Step 4.16.20.12.5.3.2
Use the power rule to combine exponents.
Step 4.16.20.12.5.3.3
Add and .
Step 4.16.20.12.5.4
Multiply by .
Step 4.16.20.12.5.5
Multiply by by adding the exponents.
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Step 4.16.20.12.5.5.1
Move .
Step 4.16.20.12.5.5.2
Use the power rule to combine exponents.
Step 4.16.20.12.5.5.3
Add and .
Step 4.16.20.12.5.6
Multiply by .
Step 4.16.20.12.6
Use the Binomial Theorem.
Step 4.16.20.12.7
Simplify each term.
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Step 4.16.20.12.7.1
Apply the product rule to .
Step 4.16.20.12.7.2
Raise to the power of .
Step 4.16.20.12.7.3
Multiply the exponents in .
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Step 4.16.20.12.7.3.1
Apply the power rule and multiply exponents, .
Step 4.16.20.12.7.3.2
Multiply by .
Step 4.16.20.12.7.4
Apply the product rule to .
Step 4.16.20.12.7.5
Raise to the power of .
Step 4.16.20.12.7.6
Multiply the exponents in .
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Step 4.16.20.12.7.6.1
Apply the power rule and multiply exponents, .
Step 4.16.20.12.7.6.2
Multiply by .
Step 4.16.20.12.7.7
Multiply by .
Step 4.16.20.12.7.8
Multiply by .
Step 4.16.20.12.7.9
Apply the product rule to .
Step 4.16.20.12.7.10
Raise to the power of .
Step 4.16.20.12.7.11
Multiply the exponents in .
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Step 4.16.20.12.7.11.1
Apply the power rule and multiply exponents, .
Step 4.16.20.12.7.11.2
Multiply by .
Step 4.16.20.12.7.12
Multiply by .
Step 4.16.20.12.7.13
Raise to the power of .
Step 4.16.20.12.7.14
Multiply by .
Step 4.16.20.12.7.15
Multiply by .
Step 4.16.20.12.7.16
Raise to the power of .
Step 4.16.20.12.7.17
Multiply by .
Step 4.16.20.12.7.18
Raise to the power of .
Step 4.16.20.12.8
Apply the distributive property.
Step 4.16.20.12.9
Simplify.
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Step 4.16.20.12.9.1
Multiply by .
Step 4.16.20.12.9.2
Multiply by .
Step 4.16.20.12.9.3
Multiply by .
Step 4.16.20.12.9.4
Multiply by .
Step 4.16.20.12.9.5
Multiply by .
Step 4.16.20.12.10
Apply the distributive property.
Step 4.16.20.12.11
Simplify.
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Step 4.16.20.12.11.1
Multiply by by adding the exponents.
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Step 4.16.20.12.11.1.1
Move .
Step 4.16.20.12.11.1.2
Use the power rule to combine exponents.
Step 4.16.20.12.11.1.3
Add and .
Step 4.16.20.12.11.2
Multiply by by adding the exponents.
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Step 4.16.20.12.11.2.1
Move .
Step 4.16.20.12.11.2.2
Use the power rule to combine exponents.
Step 4.16.20.12.11.2.3
Add and .
Step 4.16.20.12.11.3
Multiply by by adding the exponents.
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Step 4.16.20.12.11.3.1
Move .
Step 4.16.20.12.11.3.2
Use the power rule to combine exponents.
Step 4.16.20.12.11.3.3
Add and .
Step 4.16.20.12.11.4
Multiply by by adding the exponents.
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Step 4.16.20.12.11.4.1
Move .
Step 4.16.20.12.11.4.2
Use the power rule to combine exponents.
Step 4.16.20.12.11.4.3
Add and .
Step 4.16.20.13
Add and .
Step 4.16.20.14
Add and .
Step 4.16.20.15
Add and .
Step 4.16.20.16
Add and .
Step 4.16.20.17
Expand by multiplying each term in the first expression by each term in the second expression.
Step 4.16.20.18
Simplify each term.
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Step 4.16.20.18.1
Rewrite using the commutative property of multiplication.
Step 4.16.20.18.2
Multiply by by adding the exponents.
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Step 4.16.20.18.2.1
Move .
Step 4.16.20.18.2.2
Use the power rule to combine exponents.
Step 4.16.20.18.2.3
Add and .
Step 4.16.20.18.3
Multiply by .
Step 4.16.20.18.4
Rewrite using the commutative property of multiplication.
Step 4.16.20.18.5
Multiply by by adding the exponents.
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Step 4.16.20.18.5.1
Move .
Step 4.16.20.18.5.2
Use the power rule to combine exponents.
Step 4.16.20.18.5.3
Add and .
Step 4.16.20.18.6
Multiply by .
Step 4.16.20.18.7
Rewrite using the commutative property of multiplication.
Step 4.16.20.18.8
Multiply by by adding the exponents.
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Step 4.16.20.18.8.1
Move .
Step 4.16.20.18.8.2
Use the power rule to combine exponents.
Step 4.16.20.18.8.3
Add and .
Step 4.16.20.18.9
Multiply by .
Step 4.16.20.18.10
Rewrite using the commutative property of multiplication.
Step 4.16.20.18.11
Multiply by by adding the exponents.
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Step 4.16.20.18.11.1
Move .
Step 4.16.20.18.11.2
Use the power rule to combine exponents.
Step 4.16.20.18.11.3
Add and .
Step 4.16.20.18.12
Multiply by .
Step 4.16.20.18.13
Rewrite using the commutative property of multiplication.
Step 4.16.20.18.14
Multiply by by adding the exponents.
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Step 4.16.20.18.14.1
Move .
Step 4.16.20.18.14.2
Use the power rule to combine exponents.
Step 4.16.20.18.14.3
Add and .
Step 4.16.20.18.15
Multiply by .
Step 4.16.20.18.16
Multiply by .
Step 4.16.20.18.17
Multiply by .
Step 4.16.20.18.18
Multiply by .
Step 4.16.20.18.19
Multiply by .
Step 4.16.20.18.20
Multiply by .
Step 4.16.20.19
Add and .
Step 4.16.20.20
Add and .
Step 4.16.20.21
Add and .
Step 4.16.20.22
Add and .
Step 4.16.21
Add and .
Step 4.16.22
Add and .
Step 4.16.23
Add and .
Step 4.16.24
Add and .
Step 4.16.25
Add and .
Step 4.16.26
Add and .
Step 4.16.27
Add and .
Step 4.16.28
Add and .
Step 4.16.29
Add and .
Step 4.16.30
Add and .
Step 4.16.31
Add and .
Step 4.16.32
Apply the distributive property.
Step 4.16.33
Simplify.
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Step 4.16.33.1
Multiply by .
Step 4.16.33.2
Multiply by .
Step 4.16.33.3
Multiply by .
Step 4.16.33.4
Multiply by .
Step 4.16.33.5
Multiply by .
Step 4.16.33.6
Multiply by .
Step 5
The fourth derivative of with respect to is .