# Calculus Examples

Step 1

Consider the limit definition of the derivative.

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

Apply the distributive property.

Step 2.1.2.2

The final answer is .

Step 2.2

Find the components of the definition.

Step 3

Plug in the components.

Step 4

Step 4.1

Simplify the numerator.

Step 4.1.1

Multiply by .

Step 4.1.2

Add and .

Step 4.1.3

Add and .

Step 4.2

Cancel the common factor of .

Step 4.2.1

Cancel the common factor.

Step 4.2.2

Divide by .

Step 5

Evaluate the limit of which is constant as approaches .

Step 6