Question

Find the derivative: \[ \frac{d}{dx} \left[ \left| \frac{x}{4} \right| \right] \]

• A. \( |x| \)
• B. 4
• C. \( \frac{1}{2} \)
• D. \( x - 2 \)

Hint:

For derivatives involving absolute values, always express the derivative in terms of the sign function.

Answer 1

The Correct Option is B

The derivative of \( \left| \frac{x}{4} \right| \) is evaluated by first considering the absolute value function. We know that: \[ \frac{d}{dx} \left| x \right| = \frac{x}{|x|}. \] Thus, for \( \left| \frac{x}{4} \right| \), the derivative is: \[ \frac{d}{dx} \left[ \left| \frac{x}{4} \right| \right] = \frac{1}{4}. \] Therefore, the correct answer is option (B) 4.