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Calculus Examples
Step 1
Since is constant with respect to , the derivative of with respect to is .
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
Combine and .
Step 8
Multiply by .
Step 9
Multiply by .
Step 10
Factor out of .
Step 11
Step 11.1
Factor out of .
Step 11.2
Cancel the common factor.
Step 11.3
Rewrite the expression.
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
Step 15.1
Add and .
Step 15.2
Combine and .
Step 15.3
Combine and .
Step 15.4
Cancel the common factor.
Step 15.5
Simplify the expression.
Step 15.5.1
Divide by .
Step 15.5.2
Reorder the factors of .