If f(x)= x^2 |x| , write d dx (f(x) ) - Vidyadip

Question

If $\text{f}(\text{x})=\frac{\text{x}^2}{|\text{x}|},$ write $\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)$

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Answer

We have, $\frac{\text{d}}{\text{dx}}\frac{\text{x}^2}{|\text{x}|}=\begin{cases}\frac{\text{d}}{\text{dx}}\text{x}&[\text{if }\text{x}>0]\\\frac{\text{d}}{\text{dx}}(-\text{x})&[\text{if }\text{x}<0]\end{cases}$
$=\begin{cases}1&[\text{if }\text{x}>0]\\-1&[\text{if }\text{x}<0]\end{cases}$

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