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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Simplify the expression.
Step 2.6.1
Multiply by .
Step 2.6.2
Move to the left of .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Add and .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Simplify the expression.
Step 4.6.1
Multiply by .
Step 4.6.2
Move to the left of .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Simplify by adding terms.
Step 4.8.1
Multiply by .
Step 4.8.2
Subtract from .
Step 5
Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Apply the distributive property.
Step 5.4
Apply the distributive property.
Step 5.5
Combine terms.
Step 5.5.1
Multiply by .
Step 5.5.2
Multiply by .
Step 5.5.3
Raise to the power of .
Step 5.5.4
Raise to the power of .
Step 5.5.5
Use the power rule to combine exponents.
Step 5.5.6
Add and .
Step 5.5.7
Multiply by .
Step 5.5.8
Multiply by .
Step 5.5.9
Raise to the power of .
Step 5.5.10
Raise to the power of .
Step 5.5.11
Use the power rule to combine exponents.
Step 5.5.12
Add and .
Step 5.5.13
Multiply by .
Step 5.5.14
Multiply by .
Step 5.5.15
Subtract from .
Step 5.5.16
Subtract from .
Step 5.5.17
Add and .