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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
Apply the power rule and multiply exponents, .
Step 2.2
Multiply by .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Differentiate using the Power Rule which states that is where .
Step 4.5
Multiply by .
Step 4.6
By the Sum Rule, the derivative of with respect to is .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Since is constant with respect to , the derivative of with respect to is .
Step 4.9
Simplify the expression.
Step 4.9.1
Add and .
Step 4.9.2
Multiply by .
Step 4.10
Differentiate using the Power Rule which states that is where .
Step 4.11
Simplify with factoring out.
Step 4.11.1
Multiply by .
Step 4.11.2
Factor out of .
Step 4.11.2.1
Factor out of .
Step 4.11.2.2
Factor out of .
Step 4.11.2.3
Factor out of .
Step 5
Step 5.1
Factor out of .
Step 5.2
Cancel the common factor.
Step 5.3
Rewrite the expression.
Step 6
Step 6.1
Factor out of .
Step 6.2
Factor out of .
Step 7
Step 7.1
Factor out of .
Step 7.2
Cancel the common factor.
Step 7.3
Rewrite the expression.
Step 8
Step 8.1
Rewrite the expression using the negative exponent rule .
Step 8.2
Apply the distributive property.
Step 8.3
Simplify the numerator.
Step 8.3.1
Simplify each term.
Step 8.3.1.1
Expand using the FOIL Method.
Step 8.3.1.1.1
Apply the distributive property.
Step 8.3.1.1.2
Apply the distributive property.
Step 8.3.1.1.3
Apply the distributive property.
Step 8.3.1.2
Simplify and combine like terms.
Step 8.3.1.2.1
Simplify each term.
Step 8.3.1.2.1.1
Rewrite using the commutative property of multiplication.
Step 8.3.1.2.1.2
Multiply by by adding the exponents.
Step 8.3.1.2.1.2.1
Move .
Step 8.3.1.2.1.2.2
Multiply by .
Step 8.3.1.2.1.3
Move to the left of .
Step 8.3.1.2.1.4
Multiply by .
Step 8.3.1.2.1.5
Multiply by .
Step 8.3.1.2.2
Subtract from .
Step 8.3.1.3
Multiply by .
Step 8.3.1.4
Combine and .
Step 8.3.1.5
Expand using the FOIL Method.
Step 8.3.1.5.1
Apply the distributive property.
Step 8.3.1.5.2
Apply the distributive property.
Step 8.3.1.5.3
Apply the distributive property.
Step 8.3.1.6
Simplify and combine like terms.
Step 8.3.1.6.1
Simplify each term.
Step 8.3.1.6.1.1
Multiply by .
Step 8.3.1.6.1.2
Cancel the common factor of .
Step 8.3.1.6.1.2.1
Factor out of .
Step 8.3.1.6.1.2.2
Cancel the common factor.
Step 8.3.1.6.1.2.3
Rewrite the expression.
Step 8.3.1.6.1.3
Multiply by .
Step 8.3.1.6.1.4
Multiply by .
Step 8.3.1.6.1.5
Multiply .
Step 8.3.1.6.1.5.1
Combine and .
Step 8.3.1.6.1.5.2
Multiply by .
Step 8.3.1.6.2
Add and .
Step 8.3.1.7
Apply the distributive property.
Step 8.3.1.8
Simplify.
Step 8.3.1.8.1
Multiply by by adding the exponents.
Step 8.3.1.8.1.1
Move .
Step 8.3.1.8.1.2
Multiply by .
Step 8.3.1.8.2
Cancel the common factor of .
Step 8.3.1.8.2.1
Cancel the common factor.
Step 8.3.1.8.2.2
Rewrite the expression.
Step 8.3.2
Add and .
Step 8.3.3
Combine the opposite terms in .
Step 8.3.3.1
Subtract from .
Step 8.3.3.2
Add and .
Step 8.3.4
Add and .
Step 8.3.5
Add and .
Step 8.3.6
Add and .