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Calculus Examples
Step 1
Step 1.1
Rewrite as .
Step 1.2
Expand by moving outside the logarithm.
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
To apply the Chain Rule, set as .
Step 4.2
The derivative of with respect to is .
Step 4.3
Replace all occurrences of with .
Step 5
Step 5.1
Combine and .
Step 5.2
By the Sum Rule, the derivative of with respect to is .
Step 5.3
Differentiate using the Power Rule which states that is where .
Step 5.4
Since is constant with respect to , the derivative of with respect to is .
Step 5.5
Combine fractions.
Step 5.5.1
Add and .
Step 5.5.2
Combine and .
Step 5.5.3
Combine and .
Step 6
The derivative of with respect to is .
Step 7
Combine and .
Step 8
To write as a fraction with a common denominator, multiply by .
Step 9
To write as a fraction with a common denominator, multiply by .
Step 10
Step 10.1
Multiply by .
Step 10.2
Multiply by .
Step 10.3
Reorder the factors of .
Step 11
Combine the numerators over the common denominator.
Step 12
Raise to the power of .
Step 13
Raise to the power of .
Step 14
Use the power rule to combine exponents.
Step 15
Add and .
Step 16
Combine and .
Step 17
Step 17.1
Apply the distributive property.
Step 17.2
Simplify the numerator.
Step 17.2.1
Simplify each term.
Step 17.2.1.1
Simplify by moving inside the logarithm.
Step 17.2.1.2
Apply the distributive property.
Step 17.2.1.3
Multiply by .
Step 17.2.2
Apply the distributive property.
Step 17.2.3
Reorder factors in .
Step 17.3
Combine terms.
Step 17.3.1
Multiply by by adding the exponents.
Step 17.3.1.1
Multiply by .
Step 17.3.1.1.1
Raise to the power of .
Step 17.3.1.1.2
Use the power rule to combine exponents.
Step 17.3.1.2
Add and .
Step 17.3.2
Multiply by .
Step 17.4
Reorder terms.