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Calculus Examples
Step 1
Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Multiply by .
Step 5
Step 5.1
To apply the Chain Rule, set as .
Step 5.2
Differentiate using the Exponential Rule which states that is where =.
Step 5.3
Replace all occurrences of with .
Step 6
Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Simplify the expression.
Step 6.3.1
Multiply by .
Step 6.3.2
Move to the left of .
Step 6.3.3
Rewrite as .
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Combine terms.
Step 7.2.1
Combine and .
Step 7.2.2
Combine and .
Step 7.2.3
Combine and .
Step 7.2.4
Cancel the common factor of .
Step 7.2.4.1
Cancel the common factor.
Step 7.2.4.2
Rewrite the expression.
Step 7.2.5
Combine and .
Step 7.2.6
Combine and .
Step 7.2.7
Cancel the common factor of .
Step 7.2.7.1
Cancel the common factor.
Step 7.2.7.2
Rewrite the expression.
Step 7.2.8
Cancel the common factor of .
Step 7.2.8.1
Cancel the common factor.
Step 7.2.8.2
Rewrite the expression.
Step 7.3
Simplify each term.
Step 7.3.1
Separate fractions.
Step 7.3.2
Convert from to .
Step 7.3.3
Combine and .