Question

Find the derivative of \[ \frac{d}{dx} \left\{ \left| x \right|^2 \right\}. \]

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

Hint:

For differentiating absolute value functions, remember that the absolute value squared simplifies to a standard polynomial.

Answer 1

The Correct Option is B

We are given the function \( \left\{ \left| x \right|^2 \right\} \), which can be written as \( x^2 \). Taking the derivative of \( x^2 \), we get: \[ \frac{d}{dx} \left( x^2 \right) = 2x. \] Thus, the correct answer is option (B) \( 2x - 2 \).