If `f(x)=3x^(2)+5x-1`, find `f^(')(x)`

Answer

To find the derivative of the function \( f(x) = 3x^2 + 5x - 1 \), we will use the power rule of differentiation. The power rule states that if \( f(x) = ax^n \), then \( f'(x) = nax^{n-1} \).

### Step-by-Step Solution:

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

2. **Differentiate each term**:
- For the first term \( 3x^2 \):
- Apply the power rule:
\[ \frac{d}{dx}(3x^2) = 2 \cdot 3x^{2-1} = 6x \]
- For the second term \( 5x \):
- The derivative of \( 5x \) is:
\[ \frac{d}{dx}(5x) = 5 \]
- For the constant term \( -1 \):
- The derivative of a constant is:
\[ \frac{d}{dx}(-1) = 0 \]

3. **Combine the derivatives**:
\[ f'(x) = 6x + 5 + 0 \]
Thus, we have:
\[ f'(x) = 6x + 5 \]

### Final Answer:
\[ f'(x) = 6x + 5 \]