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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the Quotient 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
Differentiate using the Power Rule which states that is where .
Step 3.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4
Simplify the expression.
Step 3.4.1
Add and .
Step 3.4.2
Multiply by .
Step 3.5
By the Sum Rule, the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.8
Simplify the expression.
Step 3.8.1
Add and .
Step 3.8.2
Multiply by .
Step 3.9
By the Sum Rule, the derivative of with respect to is .
Step 3.10
Differentiate using the Power Rule which states that is where .
Step 3.11
Since is constant with respect to , the derivative of with respect to is .
Step 3.12
Differentiate using the Power Rule which states that is where .
Step 3.13
Multiply by .
Step 3.14
Since is constant with respect to , the derivative of with respect to is .
Step 3.15
Add and .
Step 4
Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
Step 4.2.1
Multiply by .
Step 4.2.2
Subtract from .
Step 4.2.3
Add and .
Step 4.2.4
Subtract from .
Step 4.3
Reorder terms.
Step 4.4
Simplify each term.
Step 4.4.1
Multiply by .
Step 4.4.2
Move to the left of .
Step 4.4.3
Multiply by .
Step 4.4.4
Factor out of .
Step 4.4.4.1
Factor out of .
Step 4.4.4.2
Factor out of .
Step 4.4.4.3
Factor out of .
Step 4.5
To write as a fraction with a common denominator, multiply by .
Step 4.6
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.6.1
Multiply by .
Step 4.6.2
Raise to the power of .
Step 4.6.3
Raise to the power of .
Step 4.6.4
Use the power rule to combine exponents.
Step 4.6.5
Add and .
Step 4.7
Combine the numerators over the common denominator.
Step 4.8
Simplify the numerator.
Step 4.8.1
Factor out of .
Step 4.8.1.1
Factor out of .
Step 4.8.1.2
Factor out of .
Step 4.8.2
Expand using the FOIL Method.
Step 4.8.2.1
Apply the distributive property.
Step 4.8.2.2
Apply the distributive property.
Step 4.8.2.3
Apply the distributive property.
Step 4.8.3
Combine the opposite terms in .
Step 4.8.3.1
Reorder the factors in the terms and .
Step 4.8.3.2
Subtract from .
Step 4.8.3.3
Add and .
Step 4.8.4
Simplify each term.
Step 4.8.4.1
Multiply by .
Step 4.8.4.2
Multiply by .
Step 4.8.5
Expand using the FOIL Method.
Step 4.8.5.1
Apply the distributive property.
Step 4.8.5.2
Apply the distributive property.
Step 4.8.5.3
Apply the distributive property.
Step 4.8.6
Simplify each term.
Step 4.8.6.1
Multiply by by adding the exponents.
Step 4.8.6.1.1
Multiply by .
Step 4.8.6.1.1.1
Raise to the power of .
Step 4.8.6.1.1.2
Use the power rule to combine exponents.
Step 4.8.6.1.2
Add and .
Step 4.8.6.2
Move to the left of .
Step 4.8.6.3
Rewrite as .
Step 4.8.6.4
Multiply by .
Step 4.8.7
Add and .
Step 4.8.8
Subtract from .
Step 4.8.9
Subtract from .
Step 4.8.10
Reorder terms.