# Calculus Examples

Find the Derivative Using Quotient Rule - d/dx
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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 3
Evaluate .
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Differentiate.
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Step 5
Simplify.
Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
Step 5.3.1
Simplify each term.
Step 5.3.1.1
Expand using the FOIL Method.
Step 5.3.1.1.1
Apply the distributive property.
Step 5.3.1.1.2
Apply the distributive property.
Step 5.3.1.1.3
Apply the distributive property.
Step 5.3.1.2
Simplify each term.
Step 5.3.1.2.1
Rewrite using the commutative property of multiplication.
Step 5.3.1.2.2
Multiply by by adding the exponents.
Step 5.3.1.2.2.1
Move .
Step 5.3.1.2.2.2
Multiply by .
Step 5.3.1.2.2.2.1
Raise to the power of .
Step 5.3.1.2.2.2.2
Use the power rule to combine exponents.
Step 5.3.1.2.2.3
Step 5.3.1.2.3
Move to the left of .
Step 5.3.1.2.4
Multiply by .
Step 5.3.1.2.5
Multiply by .
Step 5.3.1.3
Multiply by .
Step 5.3.1.4
Multiply by .
Step 5.3.1.5
Multiply by .
Step 5.3.2
Combine the opposite terms in .
Step 5.3.2.1