Question

Find the value of \( \frac{d}{dx} (3x^2 + 4x + 5) \).

• A. \( 6x + 4 \)
• B. \( 6x + 5 \)
• C. \( 3x + 4 \)
• D. \( 6x + 3 \)

Hint:

Use the power rule for differentiation: \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \).

Answer 1

The Correct Option is A

To find the derivative of the function \( f(x) = 3x^2 + 4x + 5 \), we use the power rule of differentiation. The derivative of \( 3x^2 \) is: \[ \frac{d}{dx}(3x^2) = 6x \] The derivative of \( 4x \) is: \[ \frac{d}{dx}(4x) = 4 \] The derivative of the constant 5 is 0. Thus, the derivative of \( 3x^2 + 4x + 5 \) is: \[ f'(x) = 6x + 4 \] Therefore, the correct answer is option (1).