We are given the function $h(x) = f(g(x))$, and the goal is to find $h'(2)$.

To find $h'(x)$, we need to use the chain rule since $h(x)$ is a composition of two functions, $f(x)$ and $g(x)$. The chain rule for derivatives tells us:

$h'(x) = f'(g(x)) \cdot g'(x)$

Now, we will apply this to $h'(2)$:

1. From the table, find $g(2)$. According to the table, $g(2) = 3$.
2. Now, find $f'(g(2)) = f'(3)$. According to the table, $f'(3) = 5$.
3. Finally, find $g'(2)$. From the table, $g'(2) = 5$.

Now apply the chain rule:

$h'(2) = f'(g(2)) \cdot g'(2) = f'(3) \cdot g'(2) = 5 \cdot 5 = 25$

Thus, the value of $h'(2)$ is $25$.

Do you need further clarification or have any other questions?

Here are 5 related questions to deepen your understanding:

1. How would you apply the chain rule if $h(x) = f(g(x) + x)$?
2. What happens to the derivative if $g(x)$ is a constant function?
3. Can you apply the product rule in combination with the chain rule in this scenario?
4. How would you find $h''(2)$ for the same functions?
5. What is the meaning of the chain rule in terms of rate of change for composed functions?

Tip: When using the chain rule, always start by identifying the outer function and the inner function to differentiate correctly!