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

Question

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

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Answer

We have, $\frac{\text{d}}{\text{dx}}\big\{(\text{x}+|\text{x}|)|\text{x}|\big\}=\begin{cases}\frac{\text{d}}{\text{dx}}\text{2x}^2&\big[\text{if }\text{x}>0\big]\\\frac{\text{d}}{\text{dx}}(-\text{x}+\text{x})\text{x}&\big[\text{if }\text{x}<0\big]\end{cases}$
$=\begin{cases}\text{4x}&[\text{if }\text{x}>0]\\\text{0}&[\text{if }\text{x}<0]\end{cases}$

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