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Calculus Examples
Step 1
Use to rewrite as .
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
Since is constant with respect to , the derivative of with respect to is .
Step 11
Differentiate using the Power Rule which states that is where .
Step 12
Multiply by .
Step 13
Since is constant with respect to , the derivative of with respect to is .
Step 14
Step 14.1
Add and .
Step 14.2
Combine and .
Step 14.3
Move to the left of .
Step 14.4
Factor out of .
Step 15
Step 15.1
Factor out of .
Step 15.2
Cancel the common factor.
Step 15.3
Rewrite the expression.
Step 16
Differentiate using the Power Rule which states that is where .
Step 17
Move to the left of .
Step 18
Step 18.1
Move .
Step 18.2
To write as a fraction with a common denominator, multiply by .
Step 18.3
Combine the numerators over the common denominator.
Step 19
Step 19.1
Move .
Step 19.2
Use the power rule to combine exponents.
Step 19.3
Combine the numerators over the common denominator.
Step 19.4
Add and .
Step 19.5
Divide by .
Step 20
Simplify .
Step 21
Step 21.1
Apply the distributive property.
Step 21.2
Simplify the numerator.
Step 21.2.1
Simplify each term.
Step 21.2.1.1
Rewrite using the commutative property of multiplication.
Step 21.2.1.2
Multiply by by adding the exponents.
Step 21.2.1.2.1
Move .
Step 21.2.1.2.2
Multiply by .
Step 21.2.1.3
Multiply by .
Step 21.2.1.4
Multiply by .
Step 21.2.2
Add and .
Step 21.3
Factor out of .
Step 21.3.1
Factor out of .
Step 21.3.2
Factor out of .
Step 21.3.3
Factor out of .