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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
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Multiply by .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Simplify the expression.
Step 3.6.1
Add and .
Step 3.6.2
Move to the left of .
Step 3.7
By the Sum Rule, the derivative of with respect to is .
Step 3.8
Since is constant with respect to , the derivative of with respect to is .
Step 3.9
Differentiate using the Power Rule which states that is where .
Step 3.10
Multiply by .
Step 3.11
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
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Move to the denominator using the negative exponent rule .
Step 11
Step 11.1
Apply the distributive property.
Step 11.2
Apply the distributive property.
Step 11.3
Combine terms.
Step 11.3.1
Multiply by .
Step 11.3.2
Raise to the power of .
Step 11.3.3
Raise to the power of .
Step 11.3.4
Use the power rule to combine exponents.
Step 11.3.5
Add and .
Step 11.3.6
Raise to the power of .
Step 11.3.7
Use the power rule to combine exponents.
Step 11.3.8
Write as a fraction with a common denominator.
Step 11.3.9
Combine the numerators over the common denominator.
Step 11.3.10
Add and .
Step 11.4
Reorder terms.
Step 11.5
Simplify each term.
Step 11.5.1
Expand using the FOIL Method.
Step 11.5.1.1
Apply the distributive property.
Step 11.5.1.2
Apply the distributive property.
Step 11.5.1.3
Apply the distributive property.
Step 11.5.2
Simplify each term.
Step 11.5.2.1
Multiply by .
Step 11.5.2.2
Cancel the common factor of .
Step 11.5.2.2.1
Factor out of .
Step 11.5.2.2.2
Factor out of .
Step 11.5.2.2.3
Cancel the common factor.
Step 11.5.2.2.4
Rewrite the expression.
Step 11.5.2.3
Combine and .
Step 11.5.2.4
Combine and .
Step 11.5.2.5
Move to the left of .
Step 11.5.2.6
Multiply by .
Step 11.5.2.7
Combine and .
Step 11.6
Add and .
Step 11.7
To write as a fraction with a common denominator, multiply by .
Step 11.8
Combine and .
Step 11.9
Combine the numerators over the common denominator.
Step 11.10
Simplify the numerator.
Step 11.10.1
Factor out of .
Step 11.10.1.1
Move .
Step 11.10.1.2
Factor out of .
Step 11.10.1.3
Factor out of .
Step 11.10.1.4
Factor out of .
Step 11.10.2
Multiply by .
Step 11.10.3
Add and .
Step 11.10.4
Multiply by .