If `f(x)=x^(3)-27`, then `f^(')(x)=……………………… .`

Answer

To find the derivative of the function \( f(x) = x^3 - 27 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = x^3 - 27 \]

2. **Apply the power rule for differentiation**:
The power rule states that if \( f(x) = x^n \), then the derivative \( f'(x) = n \cdot x^{n-1} \). In our case, we have two terms: \( x^3 \) and \(-27\).

3. **Differentiate each term**:
- For the term \( x^3 \):
\[ \frac{d}{dx}(x^3) = 3 \cdot x^{3-1} = 3x^2 \]
- For the constant term \(-27\):
\[ \frac{d}{dx}(-27) = 0 \]

4. **Combine the results**:
Now, we combine the derivatives of both terms:
\[ f'(x) = 3x^2 + 0 = 3x^2 \]

5. **Final answer**:
Thus, the derivative of the function is:
\[ f'(x) = 3x^2 \]