To differentiate $q^2$ with respect to $q$, we apply the power rule for differentiation. The power rule states:

$\frac{d}{dq} \left( q^n \right) = n q^{n-1}$

In your case, $q^2$ has $n = 2$. Applying the power rule:

$\frac{d}{dq} \left( q^2 \right) = 2q^{2-1} = 2q$

Thus, the derivative of $q^2$ with respect to $q$ is:

$\frac{d}{dq} \left( q^2 \right) = 2q$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the derivative of $q^3$ with respect to $q$?
2. How do you differentiate a constant times $q^n$, such as $5q^2$?
3. What is the derivative of $q^2 + 3q$ with respect to $q$?
4. How does the power rule apply to negative exponents, like $q^{-2}$?
5. What is the second derivative of $q^2$ with respect to $q$?

Tip: The power rule is one of the most fundamental rules in differentiation—it's crucial for simplifying many common functions!