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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
Raise to the power of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
Step 2.4
Factor out of .
Step 3
Move to the numerator using the negative exponent rule .
Step 4
Step 4.1
Move .
Step 4.2
Use the power rule to combine exponents.
Step 4.3
To write as a fraction with a common denominator, multiply by .
Step 4.4
To write as a fraction with a common denominator, multiply by .
Step 4.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.5.1
Multiply by .
Step 4.5.2
Multiply by .
Step 4.5.3
Multiply by .
Step 4.5.4
Multiply by .
Step 4.6
Combine the numerators over the common denominator.
Step 4.7
Add and .
Step 5
Differentiate using the Product Rule which states that is where and .
Step 6
Step 6.1
By the Sum Rule, the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Step 11.1
Move the negative in front of the fraction.
Step 11.2
Combine and .
Step 11.3
Move to the denominator using the negative exponent rule .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Step 13.1
Add and .
Step 13.2
Combine and .
Step 13.3
Move to the denominator using the negative exponent rule .
Step 14
Step 14.1
Move .
Step 14.2
Use the power rule to combine exponents.
Step 14.3
To write as a fraction with a common denominator, multiply by .
Step 14.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 14.4.1
Multiply by .
Step 14.4.2
Multiply by .
Step 14.5
Combine the numerators over the common denominator.
Step 14.6
Add and .
Step 14.7
Cancel the common factor of and .
Step 14.7.1
Factor out of .
Step 14.7.2
Cancel the common factors.
Step 14.7.2.1
Factor out of .
Step 14.7.2.2
Cancel the common factor.
Step 14.7.2.3
Rewrite the expression.
Step 15
Differentiate using the Power Rule which states that is where .
Step 16
To write as a fraction with a common denominator, multiply by .
Step 17
Combine and .
Step 18
Combine the numerators over the common denominator.
Step 19
Step 19.1
Multiply by .
Step 19.2
Subtract from .
Step 20
Move the negative in front of the fraction.
Step 21
Combine and .
Step 22
Move to the denominator using the negative exponent rule .
Step 23
To write as a fraction with a common denominator, multiply by .
Step 24
Combine and .
Step 25
Combine the numerators over the common denominator.
Step 26
Combine and .
Step 27
Multiply by .
Step 28
Combine and .
Step 29
Step 29.1
Move to the left of .
Step 29.2
Move to the denominator using the negative exponent rule .
Step 30
Step 30.1
Move .
Step 30.2
Use the power rule to combine exponents.
Step 30.3
To write as a fraction with a common denominator, multiply by .
Step 30.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 30.4.1
Multiply by .
Step 30.4.2
Multiply by .
Step 30.5
Combine the numerators over the common denominator.
Step 30.6
Add and .
Step 30.7
Cancel the common factor of and .
Step 30.7.1
Factor out of .
Step 30.7.2
Cancel the common factors.
Step 30.7.2.1
Factor out of .
Step 30.7.2.2
Cancel the common factor.
Step 30.7.2.3
Rewrite the expression.
Step 31
Factor out of .
Step 32
Step 32.1
Factor out of .
Step 32.2
Cancel the common factor.
Step 32.3
Rewrite the expression.
Step 33
Step 33.1
Apply the distributive property.
Step 33.2
Simplify the numerator.
Step 33.2.1
Simplify each term.
Step 33.2.1.1
Cancel the common factor of .
Step 33.2.1.1.1
Factor out of .
Step 33.2.1.1.2
Cancel the common factor.
Step 33.2.1.1.3
Rewrite the expression.
Step 33.2.1.2
Rewrite as .
Step 33.2.2
Write as a fraction with a common denominator.
Step 33.2.3
Combine the numerators over the common denominator.
Step 33.2.4
Add and .
Step 33.3
Combine terms.
Step 33.3.1
Multiply by .
Step 33.3.2
Combine.
Step 33.3.3
Apply the distributive property.
Step 33.3.4
Cancel the common factor of .
Step 33.3.4.1
Cancel the common factor.
Step 33.3.4.2
Rewrite the expression.
Step 33.3.5
Multiply by .
Step 33.3.6
Combine and .
Step 33.3.7
Multiply by .
Step 33.3.8
Factor out of .
Step 33.3.9
Cancel the common factors.
Step 33.3.9.1
Factor out of .
Step 33.3.9.2
Cancel the common factor.
Step 33.3.9.3
Rewrite the expression.
Step 33.3.10
Move the negative in front of the fraction.
Step 33.3.11
Multiply by .
Step 33.4
Simplify the numerator.
Step 33.4.1
To write as a fraction with a common denominator, multiply by .
Step 33.4.2
Combine the numerators over the common denominator.
Step 33.5
Multiply the numerator by the reciprocal of the denominator.
Step 33.6
Multiply .
Step 33.6.1
Multiply by .
Step 33.6.2
Multiply by by adding the exponents.
Step 33.6.2.1
Move .
Step 33.6.2.2
Use the power rule to combine exponents.
Step 33.6.2.3
To write as a fraction with a common denominator, multiply by .
Step 33.6.2.4
To write as a fraction with a common denominator, multiply by .
Step 33.6.2.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 33.6.2.5.1
Multiply by .
Step 33.6.2.5.2
Multiply by .
Step 33.6.2.5.3
Multiply by .
Step 33.6.2.5.4
Multiply by .
Step 33.6.2.6
Combine the numerators over the common denominator.
Step 33.6.2.7
Add and .
Step 33.7
Move to the left of .