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!