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The problem asks you to calculate the derivative of the function \( f(x) = x^3 + x \) at \( x = -1 \).

### Step 1: Find the derivative of the function \( f(x) \)
The derivative of \( f(x) = x^3 + x \) is calculated by applying the power rule:

\[
f'(x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(x)
\]

Using the power rule:
\[
\frac{d}{dx}(x^3) = 3x^2, \quad \frac{d}{dx}(x) = 1
\]

Thus:
\[
f'(x) = 3x^2 + 1
\]

### Step 2: Evaluate the derivative at \( x = -1 \)
Now, substitute \( x = -1 \) into the derivative:
\[
f'(-1) = 3(-1)^2 + 1 = 3(1) + 1 = 3 + 1 = 4
\]

The derivative at \( x = -1 \) is \( 4 \). However, the answer choices provided are:

- a) -2
- b) -1.5
- c) 2

It seems none of these options match the result \( 4 \). Would you like further clarification or verification on the provided options?

Here are 5 follow-up questions:
1. What is the importance of understanding the power rule for differentiation?
2. How do higher-order derivatives affect a function's graph?
3. Can we apply different methods to calculate derivatives besides the power rule?
4. How would the derivative change if the function included more complex terms?
5. What does the derivative tell us about the behavior of the function at a given point?

**Tip:** When solving derivatives, always double-check the power rule's application to avoid simple errors.

Apskaičiuokite funkcijos f(x) išvestinės reikšmę nurodytame taške: f'(-1), kai f(x) = x^3 + x

Learn how to calculate the derivative of the function f(x) = x^3 + x at the point x = -1. Understand key differentiation concepts using the power rule, suitable for high school students (Grades 10-12).

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