https://file.aiquickdraw.com/mathbot/file/1727190773607xwg76h7p.jpg

Let's solve for \( f'(x) \) using the four-step process for the given function \( f(x) = 5x^2 - 3x \).

### Step-by-step differentiation:

1. **Given function:**
   \[
   f(x) = 5x^2 - 3x
   \]

2. **Differentiate each term separately:**
   - The derivative of \( 5x^2 \) with respect to \( x \):
     \[
     \frac{d}{dx} (5x^2) = 2 \times 5x^{2-1} = 10x
     \]
   - The derivative of \( -3x \) with respect to \( x \):
     \[
     \frac{d}{dx} (-3x) = -3
     \]

3. **Final derivative \( f'(x) \):**
   \[
   f'(x) = 10x - 3
   \]

So, the correct answer is **B. \( 10x - 3 \)**.

Do you want further details on the steps? Here are some related questions to practice:

1. What is the derivative of \( 6x^3 - 4x^2 + x \)?
2. How do you differentiate a constant term like \( 5 \)?
3. What is the power rule for differentiation?
4. Can you explain the four-step process in calculus?
5. How do you apply the product rule in differentiation?

**Tip:** When differentiating powers of \( x \), remember to multiply by the exponent and reduce the power by one.

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

Learn how to find the derivative of the quadratic function f(x) = 5x^2 - 3x using the power rule of differentiation. This step-by-step solution is perfect for high school calculus students, focusing on basic differentiation techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation