Question Number 130629 by Khalmohmmad last updated on 27/Jan/21
$${y}={sgn}\left({x}\right) \\ $$$$\acute {{y}}=? \\ $$
Answered by MJS_new last updated on 27/Jan/21
$$\mathrm{sgn}\:{x}\::=\begin{cases}{−\mathrm{1};\:{x}<\mathrm{0}}\\{\mathrm{0};\:{x}=\mathrm{0}\:^{\left(\mathrm{1}\right)} }\\{\mathrm{1};\:{x}>\mathrm{0}}\end{cases} \\ $$$$\Rightarrow\:{y}'=\begin{cases}{\mathrm{0};\:{x}<\mathrm{0}}\\{\mathrm{not}\:\mathrm{defined}\:\mathrm{for}\:{x}=\mathrm{0}}\\{\mathrm{0};\:{x}>\mathrm{0}}\end{cases} \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\mathrm{if}\:\mathrm{we}\:\mathrm{define}\:\mathrm{sgn}\:\mathrm{0}\:=\mathrm{1}\:{y}'\:\mathrm{is}\:\mathrm{also}\:\mathrm{not}\:\mathrm{defined}\:\mathrm{for}\:{x}=\mathrm{0} \\ $$