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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
Differentiate using the Power Rule which states that is where .
Step 2.2
Move to the left of .
Step 2.3
By the Sum Rule, the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.6
Simplify the expression.
Step 2.6.1
Add and .
Step 2.6.2
Multiply by .
Step 3
Raise to the power of .
Step 4
Use the power rule to combine exponents.
Step 5
Add and .
Step 6
Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Simplify the numerator.
Step 6.3.1
Simplify each term.
Step 6.3.1.1
Multiply by by adding the exponents.
Step 6.3.1.1.1
Move .
Step 6.3.1.1.2
Multiply by .
Step 6.3.1.1.2.1
Raise to the power of .
Step 6.3.1.1.2.2
Use the power rule to combine exponents.
Step 6.3.1.1.3
Add and .
Step 6.3.1.2
Multiply by .
Step 6.3.2
Combine the opposite terms in .
Step 6.3.2.1
Subtract from .
Step 6.3.2.2
Add and .
Step 6.4
Move the negative in front of the fraction.
Step 6.5
Simplify the denominator.
Step 6.5.1
Rewrite as .
Step 6.5.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 6.5.3
Apply the product rule to .