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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
The derivative of with respect to is .
Step 4
Since is constant with respect to , the derivative of with respect to is .
Step 5
The derivative of with respect to is .
Step 6
Step 6.1
Multiply by .
Step 6.2
Multiply by .
Step 6.3
By the Sum Rule, the derivative of with respect to is .
Step 7
The derivative of with respect to is .
Step 8
The derivative of with respect to is .
Step 9
Step 9.1
Reorder terms.
Step 9.2
Simplify each term.
Step 9.2.1
Expand using the FOIL Method.
Step 9.2.1.1
Apply the distributive property.
Step 9.2.1.2
Apply the distributive property.
Step 9.2.1.3
Apply the distributive property.
Step 9.2.2
Simplify and combine like terms.
Step 9.2.2.1
Simplify each term.
Step 9.2.2.1.1
Multiply .
Step 9.2.2.1.1.1
Raise to the power of .
Step 9.2.2.1.1.2
Raise to the power of .
Step 9.2.2.1.1.3
Use the power rule to combine exponents.
Step 9.2.2.1.1.4
Add and .
Step 9.2.2.1.2
Multiply .
Step 9.2.2.1.2.1
Raise to the power of .
Step 9.2.2.1.2.2
Raise to the power of .
Step 9.2.2.1.2.3
Use the power rule to combine exponents.
Step 9.2.2.1.2.4
Add and .
Step 9.2.2.1.3
Multiply by by adding the exponents.
Step 9.2.2.1.3.1
Multiply by .
Step 9.2.2.1.3.1.1
Raise to the power of .
Step 9.2.2.1.3.1.2
Use the power rule to combine exponents.
Step 9.2.2.1.3.2
Add and .
Step 9.2.2.2
Add and .
Step 9.2.2.3
Subtract from .
Step 9.2.3
Factor out of .
Step 9.2.3.1
Factor out of .
Step 9.2.3.2
Factor out of .
Step 9.2.3.3
Factor out of .
Step 9.2.4
Reorder and .
Step 9.2.5
Apply pythagorean identity.
Step 9.2.6
Multiply by .
Step 9.2.7
Expand using the FOIL Method.
Step 9.2.7.1
Apply the distributive property.
Step 9.2.7.2
Apply the distributive property.
Step 9.2.7.3
Apply the distributive property.
Step 9.2.8
Simplify and combine like terms.
Step 9.2.8.1
Simplify each term.
Step 9.2.8.1.1
Multiply .
Step 9.2.8.1.1.1
Raise to the power of .
Step 9.2.8.1.1.2
Raise to the power of .
Step 9.2.8.1.1.3
Use the power rule to combine exponents.
Step 9.2.8.1.1.4
Add and .
Step 9.2.8.1.2
Multiply .
Step 9.2.8.1.2.1
Multiply by .
Step 9.2.8.1.2.2
Multiply by .
Step 9.2.8.1.2.3
Raise to the power of .
Step 9.2.8.1.2.4
Raise to the power of .
Step 9.2.8.1.2.5
Use the power rule to combine exponents.
Step 9.2.8.1.2.6
Add and .
Step 9.2.8.1.3
Multiply by by adding the exponents.
Step 9.2.8.1.3.1
Move .
Step 9.2.8.1.3.2
Multiply by .
Step 9.2.8.1.3.2.1
Raise to the power of .
Step 9.2.8.1.3.2.2
Use the power rule to combine exponents.
Step 9.2.8.1.3.3
Add and .
Step 9.2.8.1.4
Multiply .
Step 9.2.8.1.4.1
Multiply by .
Step 9.2.8.1.4.2
Multiply by .
Step 9.2.8.2
Add and .
Step 9.2.8.3
Add and .
Step 9.2.9
Factor out of .
Step 9.2.9.1
Factor out of .
Step 9.2.9.2
Factor out of .
Step 9.2.9.3
Factor out of .
Step 9.2.10
Reorder and .
Step 9.2.11
Factor out of .
Step 9.2.12
Factor out of .
Step 9.2.13
Factor out of .
Step 9.2.14
Apply pythagorean identity.
Step 9.2.15
Multiply by .
Step 9.2.16
Move to the left of .
Step 9.2.17
Rewrite as .
Step 9.3
Subtract from .