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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine and .
Step 7.3
Move to the denominator using the negative exponent rule .
Step 8
By the Sum Rule, the derivative of with respect to is .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Add and .
Step 11
Since is constant with respect to , the derivative of with respect to is .
Step 12
Differentiate using the Power Rule which states that is where .
Step 13
Step 13.1
Multiply by .
Step 13.2
Combine and .
Step 13.3
Combine and .
Step 13.4
Factor out of .
Step 14
Step 14.1
Factor out of .
Step 14.2
Cancel the common factor.
Step 14.3
Rewrite the expression.
Step 15
Move the negative in front of the fraction.