We are given the functions $f(x)$ and $g(x)$, along with their derivatives $f'(x)$ and $g'(x)$, and the table provides the corresponding values at specific points. The function $h(x)$ is defined as:

$h(x) = f(g(x))$

To find $h'(x)$, we will apply the chain rule. The derivative of $h(x) = f(g(x))$ with respect to $x$ is:

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

Now, we are asked to find $h'(1)$, so we need to compute this derivative at $x = 1$.

1. From the table, when $x = 1$:

   • $g(1) = -1$
   • $g'(1) = 2$

2. Now, using $g(1) = -1$, we find $f'(g(1)) = f'(-1)$. From the table:

   • $f'(-1) = 5$

3. Finally, using the chain rule formula:

$h'(1) = f'(g(1)) \cdot g'(1) = f'(-1) \cdot g'(1) = 5 \cdot 2 = 10$

Thus, $h'(1) = 10$.

The correct answer is: $\boxed{10}$

Would you like more details or have any further questions?

Here are some related questions you can explore:

1. What is the chain rule, and how does it apply to composite functions?
2. How would you compute $h'(2)$ for $h(x) = f(g(x))$ using the table?
3. What happens to the derivative of a function when one of its terms has a zero derivative?
4. Could you explain how the derivative of the composite function differs from simple differentiation?
5. How does the chain rule apply in multivariable calculus?

Tip: Always check the values of both the function and its derivative from a table before applying the chain rule to ensure accurate results!