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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
Differentiate using the Power Rule which states that is where .
Step 5.6
Multiply by .
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
Combine and .
Step 10
Combine the numerators over the common denominator.
Step 11
Combine and .
Step 12
Combine and .
Step 13
Step 13.1
Simplify the numerator.
Step 13.1.1
Simplify each term.
Step 13.1.1.1
Factor out of .
Step 13.1.1.1.1
Factor out of .
Step 13.1.1.1.2
Factor out of .
Step 13.1.1.1.3
Factor out of .
Step 13.1.1.2
Cancel the common factor of .
Step 13.1.1.2.1
Cancel the common factor.
Step 13.1.1.2.2
Rewrite the expression.
Step 13.1.1.3
Multiply by .
Step 13.1.2
To write as a fraction with a common denominator, multiply by .
Step 13.1.3
Combine the numerators over the common denominator.
Step 13.1.4
Simplify the numerator.
Step 13.1.4.1
Apply the distributive property.
Step 13.1.4.2
Rewrite using the commutative property of multiplication.
Step 13.1.4.3
Multiply .
Step 13.1.4.3.1
Reorder and .
Step 13.1.4.3.2
Simplify by moving inside the logarithm.
Step 13.1.4.4
Simplify by moving inside the logarithm.
Step 13.1.4.5
Apply the distributive property.
Step 13.1.4.6
Multiply .
Step 13.1.4.6.1
Reorder and .
Step 13.1.4.6.2
Simplify by moving inside the logarithm.
Step 13.1.5
Combine and .
Step 13.1.6
Reorder factors in .
Step 13.2
Combine terms.
Step 13.2.1
Rewrite as a product.
Step 13.2.2
Multiply by .
Step 13.3
Reorder terms.