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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Simplify the expression.
Step 4.2.1
Add and .
Step 4.2.2
Use to rewrite as .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 5
To write as a fraction with a common denominator, multiply by .
Step 6
Combine and .
Step 7
Combine the numerators over the common denominator.
Step 8
Step 8.1
Multiply by .
Step 8.2
Subtract from .
Step 9
Move the negative in front of the fraction.
Step 10
Step 10.1
Rewrite the expression using the negative exponent rule .
Step 10.2
Multiply by .
Step 11
Step 11.1
Apply the distributive property.
Step 11.2
Apply the distributive property.
Step 11.3
Simplify each term.
Step 11.3.1
Move to the left of .
Step 11.3.2
Multiply by .
Step 11.3.3
Cancel the common factor of .
Step 11.3.3.1
Factor out of .
Step 11.3.3.2
Factor out of .
Step 11.3.3.3
Cancel the common factor.
Step 11.3.3.4
Rewrite the expression.
Step 11.3.4
Combine and .
Step 11.3.5
Combine and .
Step 11.3.6
Move to the numerator using the negative exponent rule .
Step 11.3.7
Multiply by by adding the exponents.
Step 11.3.7.1
Move .
Step 11.3.7.2
Multiply by .
Step 11.3.7.2.1
Raise to the power of .
Step 11.3.7.2.2
Use the power rule to combine exponents.
Step 11.3.7.3
Write as a fraction with a common denominator.
Step 11.3.7.4
Combine the numerators over the common denominator.
Step 11.3.7.5
Add and .
Step 11.3.8
Move to the left of .
Step 11.3.9
Multiply by .
Step 11.3.10
Combine and .
Step 11.3.11
Move the negative in front of the fraction.
Step 11.4
Rewrite as .
Step 11.4.1
Use to rewrite as .
Step 11.4.2
Apply the power rule and multiply exponents, .
Step 11.4.3
Combine and .
Step 11.4.4
Cancel the common factor of .
Step 11.4.4.1
Cancel the common factor.
Step 11.4.4.2
Rewrite the expression.
Step 11.4.5
Simplify.
Step 11.5
Reorder terms.
Step 11.6
Simplify the numerator.
Step 11.6.1
To write as a fraction with a common denominator, multiply by .
Step 11.6.2
Combine and .
Step 11.6.3
Combine the numerators over the common denominator.
Step 11.6.4
Simplify each term.
Step 11.6.4.1
Simplify the numerator.
Step 11.6.4.1.1
Factor out of .
Step 11.6.4.1.1.1
Move .
Step 11.6.4.1.1.2
Factor out of .
Step 11.6.4.1.1.3
Rewrite as .
Step 11.6.4.1.1.4
Factor out of .
Step 11.6.4.1.2
Multiply by by adding the exponents.
Step 11.6.4.1.2.1
Move .
Step 11.6.4.1.2.2
Use the power rule to combine exponents.
Step 11.6.4.1.2.3
Combine the numerators over the common denominator.
Step 11.6.4.1.2.4
Add and .
Step 11.6.4.1.2.5
Divide by .
Step 11.6.4.1.3
Simplify .
Step 11.6.4.1.4
Multiply by .
Step 11.6.4.2
Move the negative in front of the fraction.
Step 11.6.5
To write as a fraction with a common denominator, multiply by .
Step 11.6.6
Combine and .
Step 11.6.7
Combine the numerators over the common denominator.
Step 11.6.8
Simplify the numerator.
Step 11.6.8.1
Apply the distributive property.
Step 11.6.8.2
Multiply by .
Step 11.6.8.3
Multiply by .
Step 11.6.8.4
Multiply .
Step 11.6.8.4.1
Multiply by .
Step 11.6.8.4.2
Use to rewrite as .
Step 11.6.8.4.3
Use the power rule to combine exponents.
Step 11.6.8.4.4
Combine the numerators over the common denominator.
Step 11.6.8.4.5
Add and .
Step 11.6.8.4.6
Cancel the common factor of .
Step 11.6.8.4.6.1
Cancel the common factor.
Step 11.6.8.4.6.2
Rewrite the expression.
Step 11.6.8.5
Simplify.
Step 11.6.8.6
Add and .
Step 11.7
Multiply the numerator by the reciprocal of the denominator.
Step 11.8
Multiply .
Step 11.8.1
Multiply by .
Step 11.8.2
Raise to the power of .
Step 11.8.3
Use the power rule to combine exponents.
Step 11.8.4
Write as a fraction with a common denominator.
Step 11.8.5
Combine the numerators over the common denominator.
Step 11.8.6
Add and .