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The problem asks you to compute \((f \circ u)'(2.5)\), where:

- \( f(x) = \sqrt[3]{2x^3 - x + 2} \)
- \( u(x) = \frac{x + 1}{x^2 + 2} \)

To solve this, we need to use the chain rule for differentiation. The chain rule states that:

\[
(f \circ u)'(x) = f'(u(x)) \cdot u'(x)
\]

Thus, we first need to compute:
1. \( u(2.5) \)
2. \( u'(x) \) and evaluate it at \( x = 2.5 \)
3. \( f'(x) \) and evaluate it at \( u(2.5) \)

Let's work through these steps. I’ll calculate these values step-by-step.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you want, I can guide you step by step on how to solve this problem manually or help you with any other questions. Let me know how you would like to proceed!

Here are 5 related questions to consider:
1. How do you apply the chain rule in derivative calculations?
2. What is the geometric meaning of a derivative in function composition?
3. How does implicit differentiation differ from explicit?
4. Can we derive a general formula for \( f \circ g \) for arbitrary functions?
5. How can higher-order derivatives be applied in composite functions?

**Tip:** When differentiating compositions, always carefully track inner and outer functions to apply the chain rule correctly.

Cho f(x) = √[3]{2x^3 − x + 2} và u(x) = (x + 1) / (x^2 + 2). Tính (f ∘ u)'(2.5).

Learn how to compute the derivative of a composite function using the chain rule. This example walks through finding (f ∘ u)'(2.5) where f(x) = √[3]{2x^3 − x + 2} and u(x) = (x + 1) / (x^2 + 2). Suitable for undergraduate calculus students.

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