# Calculus Examples

Consider the limit definition of the derivative.

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Apply the distributive property.

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Multiply by .

Subtract from .

Add and .

Subtract from .

Add and .

Divide by .

Evaluate the limit of which is constant as approaches .