Question

What are the steps to find the derivative of the function f(x) = 3x^2 + 2x - 5?

Answer 1

To find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \), you can follow these steps:

1. **Identify the function and its terms**: The given function consists of three terms: \( 3x^2 \), \( 2x \), and \( -5 \).

2. **Apply the power rule**: The power rule states that if you have a term of the form \( ax^n \), the derivative is \( n \cdot ax^{n-1} \).

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

4. **Combine the derivatives**: Now, combine the results from differentiating each term:
\[
f'(x) = 6x + 2 + 0 = 6x + 2
\]

5. **Conclusion**: The derivative of the function \( f(x) = 3x^2 + 2x - 5 \) is
\[
f'(x) = 6x + 2.
\]