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Calculus Examples
Step 1
Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 3
Step 3.1
Rewrite the expression using the negative exponent rule .
Step 3.2
Rewrite the expression using the negative exponent rule .
Step 3.3
Rewrite as .
Step 3.4
Expand using the FOIL Method.
Step 3.4.1
Apply the distributive property.
Step 3.4.2
Apply the distributive property.
Step 3.4.3
Apply the distributive property.
Step 3.5
Simplify and combine like terms.
Step 3.5.1
Simplify each term.
Step 3.5.1.1
Multiply by .
Step 3.5.1.2
Cancel the common factor of .
Step 3.5.1.2.1
Cancel the common factor.
Step 3.5.1.2.2
Rewrite the expression.
Step 3.5.1.3
Cancel the common factor of .
Step 3.5.1.3.1
Cancel the common factor.
Step 3.5.1.3.2
Rewrite the expression.
Step 3.5.1.4
Multiply .
Step 3.5.1.4.1
Multiply by .
Step 3.5.1.4.2
Raise to the power of .
Step 3.5.1.4.3
Raise to the power of .
Step 3.5.1.4.4
Use the power rule to combine exponents.
Step 3.5.1.4.5
Add and .
Step 3.5.2
Add and .
Step 3.6
Apply the distributive property.
Step 3.7
Simplify.
Step 3.7.1
Multiply by .
Step 3.7.2
Combine and .
Step 3.8
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3.9
Simplify each term.
Step 3.9.1
Multiply by .
Step 3.9.2
Cancel the common factor of .
Step 3.9.2.1
Move the leading negative in into the numerator.
Step 3.9.2.2
Factor out of .
Step 3.9.2.3
Cancel the common factor.
Step 3.9.2.4
Rewrite the expression.
Step 3.9.3
Multiply by .
Step 3.9.4
Multiply by .
Step 3.9.5
Multiply .
Step 3.9.5.1
Multiply by .
Step 3.9.5.2
Combine and .
Step 3.9.6
Move the negative in front of the fraction.
Step 3.9.7
Multiply by .
Step 3.9.8
Rewrite using the commutative property of multiplication.
Step 3.9.9
Multiply .
Step 3.9.9.1
Multiply by .
Step 3.9.9.2
Multiply by by adding the exponents.
Step 3.9.9.2.1
Use the power rule to combine exponents.
Step 3.9.9.2.2
Add and .
Step 3.10
Combine the numerators over the common denominator.
Step 3.11
Add and .
Step 3.12
Simplify each term.
Step 3.12.1
Move the negative in front of the fraction.
Step 3.12.2
Move the negative in front of the fraction.
Step 3.13
Add and .