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Calculus Examples
Step 1
Step 1.1
Rewrite as .
Step 1.2
Expand by moving outside the logarithm.
Step 2
Combine and .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Exponential Rule which states that is where =.
Step 3.3
Replace all occurrences of with .
Step 4
Since is constant with respect to , the derivative of with respect to is .
Step 5
Differentiate using the Quotient Rule which states that is where and .
Step 6
The derivative of with respect to is .
Step 7
Step 7.1
Combine and .
Step 7.2
Cancel the common factor of .
Step 7.2.1
Cancel the common factor.
Step 7.2.2
Rewrite the expression.
Step 7.3
Differentiate using the Power Rule which states that is where .
Step 7.4
Combine fractions.
Step 7.4.1
Multiply by .
Step 7.4.2
Combine and .
Step 7.4.3
Combine and .
Step 8
Step 8.1
Apply the distributive property.
Step 8.2
Apply the distributive property.
Step 8.3
Simplify the numerator.
Step 8.3.1
Simplify each term.
Step 8.3.1.1
Simplify by moving inside the logarithm.
Step 8.3.1.2
Multiply by .
Step 8.3.1.3
Move to the left of .
Step 8.3.1.4
Rewrite using the commutative property of multiplication.
Step 8.3.1.5
Multiply by .
Step 8.3.1.6
Simplify by moving inside the logarithm.
Step 8.3.1.7
Multiply .
Step 8.3.1.7.1
Reorder and .
Step 8.3.1.7.2
Simplify by moving inside the logarithm.
Step 8.3.2
Reorder factors in .
Step 8.4
Reorder terms.