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To solve this problem, we need to find the derivative of \( s = 1 - 3t^2 \) with respect to \( t \) and then evaluate it at \( t = -1 \).

### Step 1: Find the derivative of \( s \) with respect to \( t \)

Given:
\[
s = 1 - 3t^2
\]

To find the derivative \( \frac{ds}{dt} \), we differentiate with respect to \( t \):

\[
\frac{ds}{dt} = \frac{d}{dt} (1 - 3t^2)
\]

Applying the rules of differentiation:

\[
\frac{ds}{dt} = 0 - 6t = -6t
\]

### Step 2: Evaluate the derivative at \( t = -1 \)

Now, we substitute \( t = -1 \) into the derivative:

\[
\frac{ds}{dt} \Bigg|_{t = -1} = -6(-1) = 6
\]

### Final Answer

The value of the derivative \( \frac{ds}{dt} \) at \( t = -1 \) is **6**.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the derivative of a function using the power rule?
2. What is the geometric interpretation of a derivative?
3. How do you compute the derivative for more complex functions?
4. How do you apply the chain rule in differentiation?
5. How does the derivative change if the function is cubic or higher order?

**Tip:** When differentiating a function, always remember to apply the rules carefully, such as the power rule or product rule, depending on the structure of the function.

Find the value of the derivative \( \frac{ds}{dt} \) at \( t = -1 \) if \( s = 1 - 3t^2 \).

Learn how to find the derivative of the function \( s = 1 - 3t^2 \) and evaluate it at \( t = -1 \). This problem involves fundamental calculus concepts like differentiation using the power rule. Suitable for Grades 11-12 students.

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