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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
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 7.4
Combine and .
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
Differentiate using the Power Rule which states that is where .
Step 11
Multiply by .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Step 13.1
Add and .
Step 13.2
Combine and .
Step 13.3
Move to the left of .
Step 13.4
Cancel the common factor.
Step 13.5
Rewrite the expression.
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Multiply by .
Step 16
To write as a fraction with a common denominator, multiply by .
Step 17
Combine the numerators over the common denominator.
Step 18
Step 18.1
Use the power rule to combine exponents.
Step 18.2
Combine the numerators over the common denominator.
Step 18.3
Add and .
Step 18.4
Divide by .
Step 19
Simplify .
Step 20
Add and .