Question

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

• A. $2x + 3$
• B. $x + 3$
• C. $2x$
• D. $x^2$

Hint:

The derivative of any linear term $ax$ is simply the coefficient $a$. The derivative of a constant is always $0$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To find the derivative $f'(x)$, we use the power rule of differentiation: $\frac{d}{dx}(x^n) = nx^{n-1}$.
Step 2: Detailed Explanation:
Apply the rule to each term of the function $f(x) = x^2 + 3x$:

• For $x^2$: The derivative is $2x^{2-1} = 2x$.
• For $3x$: The derivative is $3x^{1-1} = 3(1) = 3$.

Combining these, we get $f'(x) = 2x + 3$.
Step 3: Final Answer:
The correct option is (a).