Find `f^(')` when `f(x)=x^(3)`.

Answer

To find the derivative \( f' \) of the function \( f(x) = x^3 \), we will follow the power rule of differentiation.

### Step-by-step Solution:

1. **Identify the function**:
We have \( f(x) = x^3 \).

2. **Apply the Power Rule**:
The power rule states that if \( f(x) = x^n \), then the derivative \( f'(x) \) is given by:
\[ f'(x) = n \cdot x^{n-1} \]
Here, \( n = 3 \).

3. **Differentiate**:
Using the power rule:
\[ f'(x) = 3 \cdot x^{3-1} \]
Simplifying this gives:
\[ f'(x) = 3 \cdot x^2 \]

4. **Final Answer**:
Therefore, the derivative \( f' \) when \( f(x) = x^3 \) is:
\[ f'(x) = 3x^2 \]