We are asked to find $h'(3)$, where $h(x) = f(g(x))$, and we are provided a table with values for $x$, $f(x)$, $f'(x)$, $g(x)$, and $g'(x)$.

Step-by-step approach:

1. Since $h(x) = f(g(x))$, we need to apply the chain rule to find $h'(x)$: $h'(x) = f'(g(x)) \cdot g'(x)$
2. Now, to find $h'(3)$, we need:
   • $g(3)$
   • $f'(g(3))$
   • $g'(3)$

From the table:

• $g(3) = 2$ (looking at the row for $g(x)$ where $x = 3$).
• $f'(2) = 3$ (looking at the row for $f'(x)$ where $x = 2$).
• $g'(3) = 4$ (from the row for $g'(x)$ where $x = 3$).

Now, apply the chain rule: $h'(3) = f'(g(3)) \cdot g'(3) = f'(2) \cdot g'(3) = 3 \cdot 4 = 12$

Thus, $h'(3) = 12$.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the chain rule and how does it work in general?
2. How would $h'(x)$ change if $h(x) = g(f(x))$?
3. Can we interpret $h(x) = f(g(x))$ as a composition of two functions, and how does this impact differentiation?
4. What does the derivative $g'(x)$ represent in this context?
5. How would the result differ if $f'(x)$ or $g'(x)$ were negative?

Tip: Always double-check the table for the corresponding values, as small errors in reading values can affect the final result!