# Examples of Derivative by Definition

** Example:
**Find, by definition, the derivative of function with respect to .

** Solution**:

Let

**I. **Change to and to

**II. **Find by subtraction

**III. **Divide both sides by

**IV. **Find the limit of where

This is the derivative of w.r.t .

**Example:**

Find, by definition, the derivative of function with respect to .

** Solution**:

Let

**I. **Change to and to

**II. **Find by subtraction

**III. **Divide both sides by

**IV. **Find the limit of where

This is the derivative of w.r.t .