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To find the derivative \( f'(x) \) of the function \( f(x) = 5x^2 - 3x \), you would apply the power rule to each term separately:

1. The derivative of \( 5x^2 \) is \( 10x \) because \( 2 \times 5x^{2-1} = 10x \).
2. The derivative of \( -3x \) is \(-3\) because \( 1 \times -3x^{1-1} = -3 \).

Adding these together, the derivative \( f'(x) \) of the function \( f(x) \) is \( 10x - 3 \).

Therefore, the correct answer is:
**B. 10x - 3**

If you have any more questions or need further explanations, feel free to ask! Here are some related questions you might find interesting:

1. What is the second derivative of the function \( f(x) = 5x^2 - 3x \)?
2. How would the derivative change if the function was \( f(x) = 5x^3 - 3x^2 \)?
3. Can you explain how to apply the product rule to find the derivative of \( x(5x - 3) \)?
4. What would be the derivative of \( f(x) = 5/x - 3x \)?
5. How do you find the critical points of the function \( f(x) = 5x^2 - 3x \)?

**Tip**: Remember that the power rule for differentiation states that if you have \( ax^n \), the derivative is \( anx^{n-1} \), where \( a \) is a constant and \( n \) is the power of \( x \).

Use the four-step process to find f'(x) for the function f(x) = 5x^2 - 3x.

Learn how to use the four-step process to find the derivative f'(x) for the quadratic function f(x) = 5x^2 - 3x. This solution demonstrates the power rule for differentiation and explains how to solve similar problems. Suitable for students in Grades 11-12 or early calculus courses.

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