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Calculus Examples
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Step 8.1
Move the negative in front of the fraction.
Step 8.2
Combine and .
Step 8.3
Move to the denominator using the negative exponent rule .
Step 8.4
Combine and .
Step 9
By the Sum Rule, the derivative of with respect to is .
Step 10
Differentiate using the Power Rule which states that is where .
Step 11
Since is constant with respect to , the derivative of with respect to is .
Step 12
Step 12.1
Add and .
Step 12.2
Multiply by .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Multiply by .
Step 15
To write as a fraction with a common denominator, multiply by .
Step 16
Combine and .
Step 17
Combine the numerators over the common denominator.
Step 18
Step 18.1
Move .
Step 18.2
Use the power rule to combine exponents.
Step 18.3
Combine the numerators over the common denominator.
Step 18.4
Add and .
Step 18.5
Divide by .
Step 19
Step 19.1
Simplify .
Step 19.2
Move to the left of .
Step 20
Combine and .
Step 21
Move the negative in front of the fraction.
Step 22
Step 22.1
Apply the distributive property.
Step 22.2
Apply the distributive property.
Step 22.3
Simplify the numerator.
Step 22.3.1
Simplify each term.
Step 22.3.1.1
Multiply by .
Step 22.3.1.2
Multiply .
Step 22.3.1.2.1
Multiply by .
Step 22.3.1.2.2
Multiply by .
Step 22.3.2
Add and .
Step 22.4
Factor out of .
Step 22.4.1
Factor out of .
Step 22.4.2
Factor out of .
Step 22.4.3
Factor out of .