# Calculus Examples

Consider the limit definition of the derivative.

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Add and .

Reorder and .

Add and .

The final answer is .

Reorder.

Move .

Reorder and .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Apply the distributive property.

Multiply by .

Subtract from .

Add and .

Add and .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Reduce the expression by cancelling the common factors.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Reorder and .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Split the limit using the Product of Limits Rule on the limit as approaches .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Add and .