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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Combine and .
Step 5
Step 5.1
To apply the Chain Rule, set as .
Step 5.2
Differentiate using the Power Rule which states that is where .
Step 5.3
Replace all occurrences of with .
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Step 10.1
Move the negative in front of the fraction.
Step 10.2
Combine and .
Step 10.3
Move to the denominator using the negative exponent rule .
Step 10.4
Combine and .
Step 11
By the Sum Rule, the derivative of with respect to is .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Add and .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Differentiate using the Power Rule which states that is where .
Step 16
Step 16.1
Multiply by .
Step 16.2
Combine and .
Step 16.3
Combine and .
Step 16.4
Factor out of .
Step 17
Step 17.1
Factor out of .
Step 17.2
Cancel the common factor.
Step 17.3
Rewrite the expression.
Step 18
Move the negative in front of the fraction.
Step 19
To write as a fraction with a common denominator, multiply by .
Step 20
To write as a fraction with a common denominator, multiply by .
Step 21
Step 21.1
Multiply by .
Step 21.2
Use to rewrite as .
Step 21.3
Use the power rule to combine exponents.
Step 21.4
Combine the numerators over the common denominator.
Step 21.5
Add and .
Step 21.6
Cancel the common factor of .
Step 21.6.1
Cancel the common factor.
Step 21.6.2
Rewrite the expression.
Step 21.7
Multiply by .
Step 21.8
Use to rewrite as .
Step 21.9
Use the power rule to combine exponents.
Step 21.10
Combine the numerators over the common denominator.
Step 21.11
Add and .
Step 21.12
Cancel the common factor of .
Step 21.12.1
Cancel the common factor.
Step 21.12.2
Rewrite the expression.
Step 22
Combine the numerators over the common denominator.
Step 23
Step 23.1
Use the power rule to combine exponents.
Step 23.2
Combine the numerators over the common denominator.
Step 23.3
Add and .
Step 23.4
Divide by .
Step 24
Simplify .
Step 25
Simplify.
Step 26
Step 26.1
Simplify the numerator.
Step 26.1.1
Simplify each term.
Step 26.1.1.1
Rewrite as .
Step 26.1.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 26.1.2
Reorder factors in .
Step 26.2
Reorder terms.