Question

If $ f(x) = x^2 + 3x $, then $ f'(x) $ is:

• A. \( x + 3 \)
• B. \( 2x + 3 \)
• C. \( x^2 + 3 \)
• D. \( 2x \)

Hint:

Key Fact: \( \frac{d}{dx}(x^n) = nx^{n-1} \), and \( \frac{d}{dx}(kx) = k \)

Answer 1

The Correct Option is B

To find the derivative of the function \( f(x) = x^2 + 3x \), we'll use the power rule of differentiation. The power rule states:

\(\frac{d}{dx}[x^n] = nx^{n-1}\)

Applying the power rule to each term in \( f(x) \):

1. For the term \(x^2\):
\(\frac{d}{dx}[x^2] = 2x^{2-1} = 2x\)

2. For the term \(3x\):
\(\frac{d}{dx}[3x] = 3\)

Thus, the derivative \( f'(x) \) is obtained by differentiating each term and combining them:

\(f'(x) = 2x + 3\)

Therefore, the correct answer is \(2x + 3\).

Answer 2

To solve the problem, we need to find the derivative of the function:

$f(x) = x^2 + 3x$

1. Differentiate term by term:
$\frac{d}{dx}(x^2) = 2x$
$\frac{d}{dx}(3x) = 3$

2. Combine the derivatives:
$f'(x) = 2x + 3$

Final Answer:
The derivative is $ {2x + 3} $.