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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
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
Combine and .
Step 6
Step 6.1
To apply the Chain Rule, set as .
Step 6.2
The derivative of with respect to is .
Step 6.3
Replace all occurrences of with .
Step 7
Step 7.1
Multiply by .
Step 7.2
Combine fractions.
Step 7.2.1
Multiply by .
Step 7.2.2
Combine and .
Step 7.3
Since is constant with respect to , the derivative of with respect to is .
Step 7.4
Combine and .
Step 7.5
Differentiate using the Power Rule which states that is where .
Step 7.6
Multiply by .
Step 8
Multiply by .
Step 9
Combine.
Step 10
Apply the distributive property.
Step 11
Step 11.1
Cancel the common factor.
Step 11.2
Rewrite the expression.
Step 12
Step 12.1
Simplify the numerator.
Step 12.1.1
Simplify each term.
Step 12.1.1.1
Simplify by moving inside the logarithm.
Step 12.1.1.2
Raise to the power of .
Step 12.1.2
Reorder factors in .
Step 12.2
Reorder terms.