# Calculus Examples

Step 1

Consider the difference quotient formula.

Step 2

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

Add and .

Step 2.1.2.1.3.2.1

Reorder and .

Step 2.1.2.1.3.2.2

Add and .

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

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

Add and .

Step 4.1.5

Subtract from .

Step 4.1.6

Add and .

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