Let's compute the derivatives of the given functions step by step.

(a) $f(r) = 18r$

Using the power rule:
$\frac{d}{dr} [c \cdot r^n] = c \cdot n \cdot r^{n-1}$
where $c = 18$ and $n = 1$:
$f'(r) = 18 \cdot 1 \cdot r^{1-1} = 18 \cdot r^0 = 18$
Answer:
$f'(r) = 18$

---

(b) $g(s) = 182$

Since $g(s)$ is a constant function, the derivative of any constant is 0:
$g'(s) = 0$

Answer:
$g'(s) = 0$

---

(c) $h(t) = 4t \cdot 5t$

First, simplify the function:
$h(t) = (4 \cdot 5) t \cdot t = 20t^2$
Now, differentiate using the power rule:
$h'(t) = 20 \cdot 2t^{2-1} = 40t$

Answer:
$h'(t) = 40t$

---

Do you want more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the power rule, and how does it work for different exponents?
2. How do you differentiate products of functions using the product rule?
3. What is the derivative of a sum or difference of functions?
4. How do you find the derivative of a polynomial function?
5. What happens to the derivative when a function is multiplied by a constant?

Tip: The derivative of a constant is always zero because constants do not change with respect to the variable!