To differentiate the function \( x^2 \) with respect to \( x \), we apply the power rule of differentiation. 

The power rule states that for any function of the form \( x^n \), where \( n \) is a constant, the derivative is:

\[
\frac{d}{dx}(x^n) = n \cdot x^{n-1}
\]

Applying this to \( x^2 \):

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

So, the derivative of \( x^2 \) with respect to \( x \) is \( 2x \).

Would you like more details or have any questions?

Here are some related questions:
1. What is the derivative of \( x^3 \)?
2. How do you differentiate \( 3x^4 + 2x^3 - x + 7 \)?
3. What is the derivative of a constant?
4. How do you apply the chain rule in differentiation?
5. How do you differentiate a function with respect to another variable?

**Tip:** The power rule is one of the most commonly used differentiation rules. It's a good idea to practice applying it to functions with different exponents.

Learn how to differentiate the function x^2 with respect to x using the power rule of differentiation. This detailed guide covers the application of the power rule to functions with exponents, specifically focusing on the derivative of x^2. Suitable for advanced high school students and those preparing for calculus.

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