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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 Product Rule which states that is where and .
Step 3
By the Sum Rule, the derivative of with respect to is .
Step 4
The derivative of with respect to is .
Step 5
Since is constant with respect to , the derivative of with respect to is .
Step 6
The derivative of with respect to is .
Step 7
Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 7.3
By the Sum Rule, the derivative of with respect to is .
Step 8
The derivative of with respect to is .
Step 9
The derivative of with respect to is .
Step 10
Step 10.1
Apply the distributive property.
Step 10.2
Remove parentheses.
Step 10.3
Reorder terms.
Step 10.4
Simplify each term.
Step 10.4.1
Apply the distributive property.
Step 10.4.2
Expand using the FOIL Method.
Step 10.4.2.1
Apply the distributive property.
Step 10.4.2.2
Apply the distributive property.
Step 10.4.2.3
Apply the distributive property.
Step 10.4.3
Simplify and combine like terms.
Step 10.4.3.1
Simplify each term.
Step 10.4.3.1.1
Multiply .
Step 10.4.3.1.1.1
Raise to the power of .
Step 10.4.3.1.1.2
Raise to the power of .
Step 10.4.3.1.1.3
Use the power rule to combine exponents.
Step 10.4.3.1.1.4
Add and .
Step 10.4.3.1.2
Multiply .
Step 10.4.3.1.2.1
Raise to the power of .
Step 10.4.3.1.2.2
Raise to the power of .
Step 10.4.3.1.2.3
Use the power rule to combine exponents.
Step 10.4.3.1.2.4
Add and .
Step 10.4.3.2
Reorder the factors of .
Step 10.4.3.3
Add and .
Step 10.4.4
Factor out of .
Step 10.4.5
Factor out of .
Step 10.4.6
Factor out of .
Step 10.4.7
Rearrange terms.
Step 10.4.8
Apply pythagorean identity.
Step 10.4.9
Multiply by .
Step 10.4.10
Apply the distributive property.
Step 10.4.11
Multiply by .
Step 10.4.12
Expand using the FOIL Method.
Step 10.4.12.1
Apply the distributive property.
Step 10.4.12.2
Apply the distributive property.
Step 10.4.12.3
Apply the distributive property.
Step 10.4.13
Simplify and combine like terms.
Step 10.4.13.1
Simplify each term.
Step 10.4.13.1.1
Multiply .
Step 10.4.13.1.1.1
Multiply by .
Step 10.4.13.1.1.2
Raise to the power of .
Step 10.4.13.1.1.3
Raise to the power of .
Step 10.4.13.1.1.4
Use the power rule to combine exponents.
Step 10.4.13.1.1.5
Add and .
Step 10.4.13.1.2
Multiply .
Step 10.4.13.1.2.1
Raise to the power of .
Step 10.4.13.1.2.2
Raise to the power of .
Step 10.4.13.1.2.3
Use the power rule to combine exponents.
Step 10.4.13.1.2.4
Add and .
Step 10.4.13.1.3
Multiply by .
Step 10.4.13.2
Reorder the factors of .
Step 10.4.13.3
Add and .
Step 10.4.14
Factor out of .
Step 10.4.15
Factor out of .
Step 10.4.16
Factor out of .
Step 10.4.17
Rearrange terms.
Step 10.4.18
Apply pythagorean identity.
Step 10.4.19
Multiply by .
Step 10.5
Combine the opposite terms in .
Step 10.5.1
Subtract from .
Step 10.5.2
Add and .
Step 10.6
Add and .