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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
Convert from to .
Step 6
The derivative of with respect to is .
Step 7
The derivative of with respect to is .
Step 8
Step 8.1
Apply the distributive property.
Step 8.2
Remove parentheses.
Step 8.3
Reorder terms.
Step 8.4
Simplify each term.
Step 8.4.1
Rewrite in terms of sines and cosines.
Step 8.4.2
Combine and .
Step 8.4.3
Rewrite in terms of sines and cosines.
Step 8.4.4
Multiply .
Step 8.4.4.1
Combine and .
Step 8.4.4.2
Combine and .
Step 8.4.5
Rewrite in terms of sines and cosines.
Step 8.4.6
Combine.
Step 8.4.7
Cancel the common factor of .
Step 8.4.7.1
Cancel the common factor.
Step 8.4.7.2
Rewrite the expression.
Step 8.4.8
Cancel the common factor of .
Step 8.4.8.1
Cancel the common factor.
Step 8.4.8.2
Divide by .
Step 8.4.9
Rewrite in terms of sines and cosines.
Step 8.4.10
Combine and .
Step 8.4.11
Rewrite in terms of sines and cosines.
Step 8.4.12
Apply the product rule to .
Step 8.4.13
One to any power is one.
Step 8.4.14
Combine and .
Step 8.4.15
Combine and .
Step 8.5
Simplify each term.
Step 8.5.1
Separate fractions.
Step 8.5.2
Convert from to .
Step 8.5.3
Divide by .
Step 8.5.4
Simplify the numerator.
Step 8.5.4.1
Separate fractions.
Step 8.5.4.2
Convert from to .
Step 8.5.4.3
Divide by .