If $y = x|x|$, find $\frac{dy}{dx}$ for

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Target Exam

CUET

Subject

Section B1

Chapter

Continuity and Differentiability

Question:

If $y = x|x|$, find $\frac{dy}{dx}$ for $x < 0$.

Options:

$2x$

$-2x$

$x$

$-x$

Correct Answer:

$-2x$

Explanation:

The correct answer is Option (2) → $-2x$ ##

For $x < 0$, $y=x|x| = -x^2$

$∴\frac{dy}{dx} = -2x$