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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
Apply the power rule and multiply exponents, .
Step 3.2
Cancel the common factor of .
Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 4
Simplify.
Step 5
By the Sum Rule, the derivative of with respect to is .
Step 6
Since is constant with respect to , the derivative of with respect to is .
Step 7
Differentiate using the Power Rule which states that is where .
Step 8
Multiply by .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Differentiate using the Power Rule which states that is where .
Step 11
Multiply by .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Add and .
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
To write as a fraction with a common denominator, multiply by .
Step 16
Combine and .
Step 17
Combine the numerators over the common denominator.
Step 18
Step 18.1
Multiply by .
Step 18.2
Subtract from .
Step 19
Move the negative in front of the fraction.
Step 20
Combine and .
Step 21
Move to the denominator using the negative exponent rule .
Step 22
Step 22.1
Apply the distributive property.
Step 22.2
Apply the distributive property.
Step 22.3
Apply the distributive property.
Step 22.4
Simplify the numerator.
Step 22.4.1
Simplify each term.
Step 22.4.1.1
Rewrite using the commutative property of multiplication.
Step 22.4.1.2
Multiply by by adding the exponents.
Step 22.4.1.2.1
Move .
Step 22.4.1.2.2
Multiply by .
Step 22.4.1.2.2.1
Raise to the power of .
Step 22.4.1.2.2.2
Use the power rule to combine exponents.
Step 22.4.1.2.3
Write as a fraction with a common denominator.
Step 22.4.1.2.4
Combine the numerators over the common denominator.
Step 22.4.1.2.5
Add and .
Step 22.4.1.3
Move to the left of .
Step 22.4.1.4
Multiply by .
Step 22.4.1.5
Cancel the common factor of .
Step 22.4.1.5.1
Factor out of .
Step 22.4.1.5.2
Factor out of .
Step 22.4.1.5.3
Cancel the common factor.
Step 22.4.1.5.4
Rewrite the expression.
Step 22.4.1.6
Combine and .
Step 22.4.1.7
Combine and .
Step 22.4.1.8
Move to the left of .
Step 22.4.1.9
Multiply by .
Step 22.4.1.10
Multiply .
Step 22.4.1.10.1
Combine and .
Step 22.4.1.10.2
Combine and .
Step 22.4.1.11
Move to the numerator using the negative exponent rule .
Step 22.4.1.12
Multiply by by adding the exponents.
Step 22.4.1.12.1
Move .
Step 22.4.1.12.2
Multiply by .
Step 22.4.1.12.2.1
Raise to the power of .
Step 22.4.1.12.2.2
Use the power rule to combine exponents.
Step 22.4.1.12.3
Write as a fraction with a common denominator.
Step 22.4.1.12.4
Combine the numerators over the common denominator.
Step 22.4.1.12.5
Add and .
Step 22.4.1.13
Move to the left of .
Step 22.4.1.14
Multiply by .
Step 22.4.1.15
Combine and .
Step 22.4.2
To write as a fraction with a common denominator, multiply by .
Step 22.4.3
Combine and .
Step 22.4.4
Combine the numerators over the common denominator.
Step 22.4.5
Combine the numerators over the common denominator.
Step 22.4.6
Multiply by .
Step 22.4.7
Add and .
Step 22.4.8
Simplify the numerator.
Step 22.4.8.1
Factor out of .
Step 22.4.8.1.1
Factor out of .
Step 22.4.8.1.2
Factor out of .
Step 22.4.8.1.3
Factor out of .
Step 22.4.8.2
Divide by .
Step 22.4.8.3
Simplify.
Step 22.4.9
To write as a fraction with a common denominator, multiply by .
Step 22.4.10
Combine and .
Step 22.4.11
Combine the numerators over the common denominator.
Step 22.4.12
Simplify the numerator.
Step 22.4.12.1
Factor out of .
Step 22.4.12.1.1
Move .
Step 22.4.12.1.2
Factor out of .
Step 22.4.12.1.3
Factor out of .
Step 22.4.12.2
Multiply by .
Step 22.4.12.3
Add and .
Step 22.4.13
To write as a fraction with a common denominator, multiply by .
Step 22.4.14
Multiply by .
Step 22.4.15
Combine the numerators over the common denominator.
Step 22.4.16
Simplify the numerator.
Step 22.4.16.1
Multiply by by adding the exponents.
Step 22.4.16.1.1
Move .
Step 22.4.16.1.2
Use the power rule to combine exponents.
Step 22.4.16.1.3
Combine the numerators over the common denominator.
Step 22.4.16.1.4
Add and .
Step 22.4.16.1.5
Divide by .
Step 22.4.16.2
Simplify .
Step 22.4.16.3
Apply the distributive property.
Step 22.4.16.4
Rewrite using the commutative property of multiplication.
Step 22.4.16.5
Move to the left of .
Step 22.4.16.6
Multiply by by adding the exponents.
Step 22.4.16.6.1
Move .
Step 22.4.16.6.2
Multiply by .
Step 22.4.17
Factor out of .
Step 22.4.18
Factor out of .
Step 22.4.19
Factor out of .
Step 22.4.20
Rewrite as .
Step 22.4.21
Factor out of .
Step 22.4.22
Rewrite as .
Step 22.4.23
Move the negative in front of the fraction.
Step 22.5
Combine terms.
Step 22.5.1
Rewrite as a product.
Step 22.5.2
Multiply by .
Step 22.5.3
Raise to the power of .
Step 22.5.4
Use the power rule to combine exponents.
Step 22.5.5
Write as a fraction with a common denominator.
Step 22.5.6
Combine the numerators over the common denominator.
Step 22.5.7
Add and .