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To solve the problem, we need to find the derivative of \( h(x) = (f(x))^2 \) and then evaluate it at \( x = 2 \).

### Step 1: Differentiate \( h(x) \)

The function \( h(x) = (f(x))^2 \) is a composition of functions, so we need to apply the chain rule to differentiate it:

\[
h'(x) = 2f(x) \cdot f'(x)
\]

### Step 2: Substitute the given values

Now, we substitute \( x = 2 \), \( f(2) = 4 \), and \( f'(2) = 5 \):

\[
h'(2) = 2 \cdot f(2) \cdot f'(2)
\]

Substitute the given values:

\[
h'(2) = 2 \cdot 4 \cdot 5
\]

### Step 3: Calculate the value

\[
h'(2) = 2 \cdot 20 = 40
\]

### Final Answer

The value of \( h'(2) \) is **40**.

Would you like more details, or do you have any questions?

### Related Questions
1. What is the chain rule in calculus, and how is it applied to functions?
2. How do you find the derivative of a composite function?
3. What is the significance of the derivative at a specific point?
4. Can you solve for \( h'(x) \) if \( h(x) = f(x)g(x) \) and both \( f(x) \) and \( g(x) \) are given?
5. How does the product rule differ from the chain rule?

### Tip
When differentiating a function that involves another function raised to a power, remember to use the chain rule by differentiating the outer function first and then multiplying by the derivative of the inner function.

Given f(2) = 4 and f'(2) = 5, find the value of h'(2) based on the function h(x) = (f(x))^2.

Learn how to solve for the derivative h'(x) of the function h(x) = (f(x))^2 at x = 2 using the chain rule. In this problem, f(2) = 4 and f'(2) = 5 are given, and we calculate the value of h'(2) step-by-step.

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