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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
Differentiate using the Power Rule which states that is where .
Step 3.2
Move to the left of .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Differentiate using the Power Rule which states that is where .
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
Combine and .
Step 8.4
Move to the denominator using the negative exponent rule .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Step 10.1
Add and .
Step 10.2
Combine and .
Step 10.3
Simplify the expression.
Step 10.3.1
Move to the left of .
Step 10.3.2
Move to the numerator using the negative exponent rule .
Step 11
Step 11.1
Move .
Step 11.2
Use the power rule to combine exponents.
Step 11.3
To write as a fraction with a common denominator, multiply by .
Step 11.4
Combine and .
Step 11.5
Combine the numerators over the common denominator.
Step 11.6
Simplify the numerator.
Step 11.6.1
Multiply by .
Step 11.6.2
Add and .
Step 12
Step 12.1
Move .
Step 12.2
To write as a fraction with a common denominator, multiply by .
Step 12.3
Combine and .
Step 12.4
Combine the numerators over the common denominator.
Step 13
Multiply by .
Step 14
Step 14.1
Apply the distributive property.
Step 14.2
Simplify the numerator.
Step 14.2.1
Simplify each term.
Step 14.2.1.1
Rewrite using the commutative property of multiplication.
Step 14.2.1.2
Multiply by by adding the exponents.
Step 14.2.1.2.1
Move .
Step 14.2.1.2.2
Multiply by .
Step 14.2.1.2.2.1
Raise to the power of .
Step 14.2.1.2.2.2
Use the power rule to combine exponents.
Step 14.2.1.2.3
Write as a fraction with a common denominator.
Step 14.2.1.2.4
Combine the numerators over the common denominator.
Step 14.2.1.2.5
Add and .
Step 14.2.1.3
Multiply by .
Step 14.2.1.4
Multiply by .
Step 14.2.2
Add and .
Step 14.3
Factor out of .
Step 14.3.1
Factor out of .
Step 14.3.2
Factor out of .
Step 14.3.3
Factor out of .