To solve the problem using the definition of the derivative, the derivative of $f(x)$ is calculated as:

$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Here, $f(x) = 3x + 2$. Let us calculate step by step:

1. Substitute $f(x + h)$ and $f(x)$ into the definition: $f(x + h) = 3(x + h) + 2 = 3x + 3h + 2$ $f(x) = 3x + 2$

   The difference is: $f(x + h) - f(x) = (3x + 3h + 2) - (3x + 2) = 3h$

2. Divide by $h$: $\frac{f(x + h) - f(x)}{h} = \frac{3h}{h} = 3$

3. Take the limit as $h \to 0$: $f'(x) = \lim_{h \to 0} 3 = 3$

Thus, the derivative is:

$f'(x) = 3$

Would you like me to clarify any steps or explain further? Here are some related questions to explore the topic:

1. What is the significance of using the definition of the derivative?
2. How do derivatives represent the slope of a function at a given point?
3. Can the same process be applied to non-linear functions? How does it differ?
4. What happens when $f(x)$ is a constant function, like $f(x) = 5$?
5. How can we use the derivative to find the equation of the tangent line at a point?

Tip: For linear functions, the derivative is always equal to the slope of the line, as the rate of change is constant.