Write the value of d dx (x|x|) - Vidyadip

Question

Write the value of $\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)$

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Answer

We have, $\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)=\begin{cases}\frac{\text{d}}{\text{dx}}\text{x}^2&\big[\text{if }\text{x}>0\big]\\\frac{\text{d}}{\text{dx}}(-\text{x})\text{x}&\big[\text{if }\text{x}<0\big]\end{cases}$
$=\begin{cases}\text{2x}&[\text{if }\text{x}>0]\\-\text{2x}&[\text{if }\text{x}<0]\end{cases}$

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