The Derivative (R) Question $$ 2,9,4.11 $$ Part 1 of 3 Find the indicated quantities for $$ f(x)=3 x^{2} $$.

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Sure, let's work through **Part 1** of your derivative question for the function $$ f(x) = 3x^{2} $$.

### **1. Find the Derivative $$ f'(x) $$**

To find the derivative of $$ f(x) = 3x^{2} $$, we'll use the **power rule** of differentiation. The power rule states:

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

Let's apply this step-by-step:

1. **Identify the components:**
   - **Coefficient (constant factor):** 3
   - **Variable part:** $$ x^2 $$
   - **Exponent (n):** 2

2. **Apply the power rule:**
   $$
   f'(x) = \frac{d}{dx} [3x^{2}] = 3 \cdot \frac{d}{dx} [x^{2}]
   $$
   $$
   \frac{d}{dx} [x^{2}] = 2x^{2-1} = 2x
   $$

3. **Combine the results:**
   $$
   f'(x) = 3 \cdot 2x = 6x
   $$

### **Summary**

- **Original Function:** $$ f(x) = 3x^{2} $$
- **First Derivative:** $$ f'(x) = 6x $$

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If **Part 1** includes additional "indicated quantities," feel free to provide more details, and I'll be happy to assist further!
The derivative of $$ f(x) = 3x^{2} $$ is $$ f'(x) = 6x $$.

The Derivative (R) Question \( 2,9,4.11 \) Part 1 of 3 Find the indicated quantities for \( f(x)=3 x^{2} \).

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