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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
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
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 8.4
Combine and .
Step 9
By the Sum Rule, the derivative of with respect to is .
Step 10
Since is constant with respect to , the derivative of with respect to is .
Step 11
Differentiate using the Power Rule which states that is where .
Step 12
Multiply by .
Step 13
Since is constant with respect to , the derivative of with respect to is .
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Multiply by .
Step 16
Differentiate using the Power Rule which states that is where .
Step 17
Multiply by .
Step 18
Step 18.1
Reorder terms.
Step 18.2
Simplify each term.
Step 18.2.1
Multiply by .
Step 18.2.2
Factor out of .
Step 18.2.3
Cancel the common factors.
Step 18.2.3.1
Factor out of .
Step 18.2.3.2
Cancel the common factor.
Step 18.2.3.3
Rewrite the expression.
Step 18.3
To write as a fraction with a common denominator, multiply by .
Step 18.4
Combine the numerators over the common denominator.
Step 18.5
Simplify the numerator.
Step 18.5.1
Apply the distributive property.
Step 18.5.2
Multiply by by adding the exponents.
Step 18.5.2.1
Move .
Step 18.5.2.2
Multiply by .
Step 18.5.3
Multiply by by adding the exponents.
Step 18.5.3.1
Use the power rule to combine exponents.
Step 18.5.3.2
Combine the numerators over the common denominator.
Step 18.5.3.3
Add and .
Step 18.5.3.4
Divide by .
Step 18.5.4
Simplify .
Step 18.5.5
Add and .
Step 18.5.6
Subtract from .
Step 18.5.7
Factor out of .
Step 18.5.7.1
Factor out of .
Step 18.5.7.2
Factor out of .
Step 18.5.7.3
Factor out of .
Step 18.6
Factor out of .
Step 18.7
Rewrite as .
Step 18.8
Factor out of .
Step 18.9
Rewrite as .
Step 18.10
Move the negative in front of the fraction.