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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
Step 3.1
Move to the left of .
Step 3.2
By the Sum Rule, the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Differentiate using the Power Rule which states that is where .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Add and .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
Step 5.1
Move to the left of .
Step 5.2
By the Sum Rule, the derivative of with respect to is .
Step 5.3
Since is constant with respect to , the derivative of with respect to is .
Step 5.4
Differentiate using the Power Rule which states that is where .
Step 5.5
Multiply by .
Step 5.6
Since is constant with respect to , the derivative of with respect to is .
Step 5.7
Simplify the expression.
Step 5.7.1
Add and .
Step 5.7.2
Multiply by .
Step 6
Step 6.1
Factor out of .
Step 6.1.1
Factor out of .
Step 6.1.2
Factor out of .
Step 6.1.3
Factor out of .
Step 6.2
Reorder the factors of .