https://file.aiquickdraw.com/mathbot/file/1728891872760a6o1ms4x.jpg

The expression in the image shows the derivative of \( x^3 \) with respect to \( x \), written as:

\[
\frac{d}{dx}(x^3)
\]

To find the derivative of \( x^3 \), we apply the power rule for differentiation. The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).

In this case, \( n = 3 \), so:

\[
\frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2
\]

Thus, the derivative is:

\[
3x^2
\]

Would you like a detailed explanation of the power rule or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you apply the power rule to negative exponents?
2. What is the derivative of \( x^n \) when \( n \) is a fraction?
3. How would you differentiate a more complex polynomial, such as \( 2x^4 + 3x^3 - x + 7 \)?
4. Can you explain the chain rule and how it applies to functions of functions?
5. How would you find the second derivative of \( x^3 \)?

**Tip**: When differentiating, always remember to reduce the power by 1 and multiply by the original power when using the power rule!

What is the derivative of x^3 with respect to x?

Learn how to find the derivative of x^3 using the power rule for differentiation. This solution explains the key concepts and formulas involved, suitable for high school students in Grades 9-12.

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