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Calculus Examples
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
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
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
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
Move to the denominator 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
To write as a fraction with a common denominator, multiply by .
Step 11.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 11.5.1
Multiply by .
Step 11.5.2
Multiply by .
Step 11.5.3
Multiply by .
Step 11.5.4
Multiply by .
Step 11.6
Combine the numerators over the common denominator.
Step 11.7
Add and .
Step 12
Differentiate using the Power Rule which states that is where .
Step 13
To write as a fraction with a common denominator, multiply by .
Step 14
Combine and .
Step 15
Combine the numerators over the common denominator.
Step 16
Step 16.1
Multiply by .
Step 16.2
Subtract from .
Step 17
Move the negative in front of the fraction.
Step 18
Combine and .
Step 19
Move to the denominator using the negative exponent rule .
Step 20
To write as a fraction with a common denominator, multiply by .
Step 21
Combine and .
Step 22
Combine the numerators over the common denominator.
Step 23
Combine and .
Step 24
Combine and .
Step 25
Step 25.1
Move to the left of .
Step 25.2
Move to the denominator using the negative exponent rule .
Step 26
Step 26.1
Move .
Step 26.2
Use the power rule to combine exponents.
Step 26.3
To write as a fraction with a common denominator, multiply by .
Step 26.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 26.4.1
Multiply by .
Step 26.4.2
Multiply by .
Step 26.5
Combine the numerators over the common denominator.
Step 26.6
Simplify the numerator.
Step 26.6.1
Multiply by .
Step 26.6.2
Add and .
Step 26.7
Cancel the common factor of and .
Step 26.7.1
Factor out of .
Step 26.7.2
Cancel the common factors.
Step 26.7.2.1
Factor out of .
Step 26.7.2.2
Cancel the common factor.
Step 26.7.2.3
Rewrite the expression.
Step 27
Step 27.1
Apply the distributive property.
Step 27.2
Simplify the numerator.
Step 27.2.1
Simplify each term.
Step 27.2.1.1
Cancel the common factor of .
Step 27.2.1.1.1
Factor out of .
Step 27.2.1.1.2
Cancel the common factor.
Step 27.2.1.1.3
Rewrite the expression.
Step 27.2.1.2
Cancel the common factor of .
Step 27.2.1.2.1
Cancel the common factor.
Step 27.2.1.2.2
Rewrite the expression.
Step 27.2.2
Write as a fraction with a common denominator.
Step 27.2.3
Combine the numerators over the common denominator.
Step 27.2.4
Add and .
Step 27.3
Combine terms.
Step 27.3.1
Multiply by .
Step 27.3.2
Combine.
Step 27.3.3
Apply the distributive property.
Step 27.3.4
Cancel the common factor of .
Step 27.3.4.1
Factor out of .
Step 27.3.4.2
Cancel the common factor.
Step 27.3.4.3
Rewrite the expression.
Step 27.3.5
Cancel the common factor of .
Step 27.3.5.1
Factor out of .
Step 27.3.5.2
Cancel the common factor.
Step 27.3.5.3
Rewrite the expression.
Step 27.3.6
Multiply by .
Step 27.3.7
Move to the left of .
Step 27.3.8
Multiply by .
Step 27.3.9
Multiply by by adding the exponents.
Step 27.3.9.1
Move .
Step 27.3.9.2
Use the power rule to combine exponents.
Step 27.3.9.3
To write as a fraction with a common denominator, multiply by .
Step 27.3.9.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 27.3.9.4.1
Multiply by .
Step 27.3.9.4.2
Multiply by .
Step 27.3.9.5
Combine the numerators over the common denominator.
Step 27.3.9.6
Add and .
Step 27.3.9.7
Cancel the common factor of and .
Step 27.3.9.7.1
Factor out of .
Step 27.3.9.7.2
Cancel the common factors.
Step 27.3.9.7.2.1
Factor out of .
Step 27.3.9.7.2.2
Cancel the common factor.
Step 27.3.9.7.2.3
Rewrite the expression.