https://file.aiquickdraw.com/mathbot/file/1726053655941vpyfbnnr.jpg

Let's examine the image closely:

The function given is:
\[
f(x) = 2x^3 - x^2 + 3x
\]
The problem asks for the derivative of \( f(x) \), denoted by \( f'(x) \).

The derivative provided is:
\[
f'(x) = 6x^2 - 2x + 3
\]

Now, let's compute the derivative to verify the result:
- The derivative of \( 2x^3 \) is \( 6x^2 \).
- The derivative of \( -x^2 \) is \( -2x \).
- The derivative of \( 3x \) is \( 3 \).

So the correct derivative is indeed:
\[
f'(x) = 6x^2 - 2x + 3
\]

Everything in the solution is correct.

Would you like a more detailed explanation of how the derivatives were computed, or do you have any other questions?

Here are some related questions you might want to explore:
1. How do you find higher-order derivatives of this function?
2. What is the interpretation of the derivative \( f'(x) \) in practical terms?
3. Can you find the critical points of this function by solving \( f'(x) = 0 \)?
4. How do you determine the concavity of the graph of \( f(x) \)?
5. What is the equation of the tangent line to the graph at a particular point?

**Tip:** Always check each term's power when differentiating polynomial functions to avoid simple mistakes.

Find the derivative of the function f(x) = 2x^3 - x^2 + 3x.

Learn how to differentiate the function f(x) = 2x^3 - x^2 + 3x using the power rule for derivatives. This problem covers key concepts in calculus and is suitable for students in Grades 11-12 or early college level.

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