# Calculus Examples

Find the Difference Quotient
Step 1
Consider the difference quotient formula.
Step 2
Find the components of the definition.
Step 2.1
Evaluate the function at .
Step 2.1.1
Replace the variable with in the expression.
Step 2.1.2
Simplify the result.
Step 2.1.2.1
Simplify each term.
Step 2.1.2.1.1
Rewrite as .
Step 2.1.2.1.2
Expand using the FOIL Method.
Step 2.1.2.1.2.1
Apply the distributive property.
Step 2.1.2.1.2.2
Apply the distributive property.
Step 2.1.2.1.2.3
Apply the distributive property.
Step 2.1.2.1.3
Simplify and combine like terms.
Step 2.1.2.1.3.1
Simplify each term.
Step 2.1.2.1.3.1.1
Multiply by .
Step 2.1.2.1.3.1.2
Multiply by .
Step 2.1.2.1.3.2
Step 2.1.2.1.3.2.1
Reorder and .
Step 2.1.2.1.3.2.2
Step 2.1.2.2
The final answer is .
Step 2.2
Reorder.
Step 2.2.1
Move .
Step 2.2.2
Reorder and .
Step 2.3
Find the components of the definition.
Step 3
Plug in the components.
Step 4
Simplify.
Step 4.1
Simplify the numerator.
Step 4.1.1
Apply the distributive property.
Step 4.1.2
Multiply by .
Step 4.1.3
Subtract from .
Step 4.1.4
Step 4.1.5
Subtract from .
Step 4.1.6
Step 4.1.7
Factor out of .
Step 4.1.7.1
Factor out of .
Step 4.1.7.2
Factor out of .
Step 4.1.7.3
Factor out of .
Step 4.2
Reduce the expression by cancelling the common factors.
Step 4.2.1
Cancel the common factor of .
Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Divide by .
Step 4.2.2
Reorder and .
Step 5