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To find \( g'(t) \) for the given function \( g(t) = \frac{8}{t^2} \), we can rewrite the function in a more differentiable form using negative exponents.

\[
g(t) = 8t^{-2}
\]

Now, differentiate using the power rule. The power rule states that if \( f(t) = t^n \), then \( f'(t) = n \cdot t^{n-1} \).

Applying the power rule to \( g(t) = 8t^{-2} \):

\[
g'(t) = 8 \cdot (-2) \cdot t^{-3}
\]
\[
g'(t) = -16t^{-3}
\]

This can also be written as:

\[
g'(t) = \frac{-16}{t^3}
\]

So, \( g'(t) = \frac{-16}{t^3} \).

Would you like more details on any step, or have any other questions?

### Related Questions:
1. How do you apply the chain rule in differentiation?
2. What is the derivative of \( \frac{1}{t^n} \)?
3. Can the product rule be used for this function, and how would it differ?
4. How do higher-order derivatives of functions like \( t^{-2} \) look?
5. What is the geometric interpretation of the derivative for rational functions?

**Tip:** When differentiating functions, simplifying exponents to negative powers can often make the process easier, especially for applying basic rules like the power rule.

Find g'(t) for the function g(t) = 8/t^2.

Learn how to differentiate the function g(t) = 8/t^2 using the power rule. This calculus problem involves rewriting the function with negative exponents and applying the differentiation rule for powers of t. Suitable for students in Grades 11-12.

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