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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 Exponential Rule which states that is where =.
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Step 4.1
Rewrite as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Multiply.
Step 4.3.1
Multiply by .
Step 4.3.2
Multiply by .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Simplify the expression.
Step 4.5.1
Multiply by .
Step 4.5.2
Add and .
Step 5
Step 5.1
Move .
Step 5.2
Use the power rule to combine exponents.
Step 5.3
Add and .
Step 6
Simplify .
Step 7
Differentiate using the Power Rule which states that is where .
Step 8
Step 8.1
Reorder terms.
Step 8.2
Reorder factors in .