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  • Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 12 maths

Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 12 maths

Answers (1)

Answer:

The answer of the given question will be -2x.

Given:

\text { If } y=x|x| \text { find } \frac{d y}{d x} \text { for } x<0

Hint:

|x|=\left\{\begin{array}{cc} x, & x \geq 0 \\ -x, & x<0 \end{array}\right\}

Solution:  

\begin{aligned} &y=x|x| \\\\ &y=x(-x,) \text { since } x<0 \\\\ &=-x^{2} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=-\frac{d}{d x}\left(x^{2}\right)=-2 x \\\\ &\text { So, the } \frac{d y}{d x}=-2 x \end{aligned}

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