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f-x-sgn-x-f-x-d-dx-f-x-




Question Number 204688 by Davidtim last updated on 25/Feb/24
f(x)=sgn(x);     f^′ (x)=(d/dx)[f(x)]=?
$${f}\left({x}\right)={sgn}\left({x}\right);\:\:\:\:\:{f}^{'} \left({x}\right)=\frac{{d}}{{dx}}\left[{f}\left({x}\right)\right]=? \\ $$
Answered by Faetmaaa last updated on 27/Feb/24
(d/dx)[f∣_(]−∞, 0[) (x)] = (d/dx)[f∣_(]0, +∞[) (x)] = 0
$$\frac{\mathrm{d}}{\mathrm{d}{x}}\left[{f}\mid_{\left.\right]−\infty,\:\mathrm{0}\left[\right.} \left({x}\right)\right]\:=\:\frac{\mathrm{d}}{\mathrm{d}{x}}\left[{f}\mid_{\left.\right]\mathrm{0},\:+\infty\left[\right.} \left({x}\right)\right]\:=\:\mathrm{0} \\ $$

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