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Calculus Examples
Step 1
Differentiate using the Product 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
Rewrite as .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Subtract from .
Step 8
By the Sum Rule, the derivative of with respect to is .
Step 9
Differentiate using the Power Rule which states that is where .
Step 10
Since is constant with respect to , the derivative of with respect to is .
Step 11
Step 11.1
Add and .
Step 11.2
Multiply by .
Step 12
By the Sum Rule, the derivative of with respect to is .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Add and .
Step 16
Rewrite the expression using the negative exponent rule .
Step 17
Step 17.1
Combine terms.
Step 17.1.1
Combine and .
Step 17.1.2
Move the negative in front of the fraction.
Step 17.1.3
Combine and .
Step 17.1.4
Move to the left of .
Step 17.1.5
Combine and .
Step 17.1.6
To write as a fraction with a common denominator, multiply by .
Step 17.1.7
Combine the numerators over the common denominator.
Step 17.1.8
Multiply by .
Step 17.2
Reorder terms.