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To find \( h'(2) \) using the given chart and the fact that \( h(x) = f(g(x)) \), we apply the chain rule for derivatives:

\[
h'(x) = f'(g(x)) \cdot g'(x)
\]

### Step-by-step solution:

1. **Evaluate \( g(2) \):**
   From the chart, \( g(2) = -5 \).

2. **Evaluate \( g'(2) \):**
   From the chart, \( g'(2) = -4 \).

3. **Evaluate \( f'(g(2)) \):**
   Since \( g(2) = -5 \), we find \( f'(-5) \) from the chart. From the chart, \( f'(-5) = 7 \).

4. **Combine results:**
   Using the chain rule formula:
   \[
   h'(2) = f'(g(2)) \cdot g'(2)
   \]
   Substituting the values:
   \[
   h'(2) = f'(-5) \cdot g'(2) = 7 \cdot (-4) = -28
   \]

### Final Answer:
\[
h'(2) = -28
\]

Would you like a more detailed explanation or help with a related question?  

### Related Questions:
1. What is the general application of the chain rule in composite functions?
2. How would the process change if \( h(x) = g(f(x)) \)?
3. Can you explain the significance of the derivative of \( g(x) \) in this problem?
4. What happens to \( h'(x) \) if \( g'(x) \) is zero at some point?
5. How can this method be extended to higher-order derivatives of \( h(x) \)?

### Tip:
When dealing with composite functions, always identify the inner and outer functions first to correctly apply the chain rule.

Use the chart to find h'(2) in simplest form, where h(x) = f(g(x)).

Learn how to find h'(2) where h(x) = f(g(x)) using a provided chart of function values and derivatives. This calculus problem involves applying the chain rule to composite functions, using specific values from the chart for accurate computation.

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