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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
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
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Simplify the expression.
Step 2.4.1
Add and .
Step 2.4.2
Move to the left of .
Step 2.5
By the Sum Rule, the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Since is constant with respect to , the derivative of with respect to is .
Step 2.8
Simplify the expression.
Step 2.8.1
Add and .
Step 2.8.2
Multiply by .
Step 3
Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 3.4
Simplify the numerator.
Step 3.4.1
Simplify each term.
Step 3.4.1.1
Multiply by by adding the exponents.
Step 3.4.1.1.1
Move .
Step 3.4.1.1.2
Multiply by .
Step 3.4.1.2
Multiply by .
Step 3.4.1.3
Multiply by .
Step 3.4.2
Subtract from .
Step 3.5
Factor using the perfect square rule.
Step 3.5.1
Rewrite as .
Step 3.5.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 3.5.3
Rewrite the polynomial.
Step 3.5.4
Factor using the perfect square trinomial rule , where and .
Step 3.6
Cancel the common factor of .
Step 3.6.1
Cancel the common factor.
Step 3.6.2
Rewrite the expression.