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We are given the following information:

- \( f'(-3) = -10 \)
- \( g(x) = -8f(x) \)

We need to find \( g'(-3) \).

### Step 1: Differentiate \( g(x) \)
Given \( g(x) = -8f(x) \), we can differentiate both sides of this equation with respect to \( x \).

\[
g'(x) = -8f'(x)
\]

### Step 2: Plug in the value \( x = -3 \)
Substitute \( f'(-3) = -10 \) into the derivative we just found:

\[
g'(-3) = -8(-10)
\]

\[
g'(-3) = 80
\]

### Final Answer:
\[
g'(-3) = 80
\]

Would you like more details or have any further questions? 

Here are some related questions to consider:
1. How do we differentiate functions using the chain rule?
2. What does it mean to differentiate a function like \( g(x) = -8f(x) \)?
3. How do we apply the product rule in cases with more complicated products?
4. What happens when functions have constants multiplied by them?
5. Can we use this method for other composite functions?

**Tip:** When differentiating a function multiplied by a constant, the constant remains and you only differentiate the variable function.

If f'(-3) = -10, and g(x) = -8f(x), what is g'(-3)?

Learn how to find g'(-3) when f'(-3) = -10 and g(x) = -8f(x). This solution involves differentiation and calculating derivatives of functions with constant multipliers. Ideal for students in Grades 11-12.

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