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!

Understand how to differentiate q^2 with respect to q using the power rule in calculus. This step-by-step guide explains the application of the formula d/dq(q^n) = n*q^(n-1) and explores related questions. Suitable for high school students in Grades 10-12.

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