y-x-x-find-y-

Question Number 83413 by jagoll last updated on 02/Mar/20

y = x ∣ x ∣

find y^{'} ?

Commented by mr W last updated on 02/Mar/20

∣ x ∣= s i g n (x) x

y = s i g n (x) x^{2}

y^{'} = s i g n (x) 2 x + x^{2} {(s i g n (x))}^{'}

= 2 s i g n (x) x

= 2 ∣ x ∣

Commented by Kunal12588 last updated on 02/Mar/20

w h a t i s s i g n (x) ? s i g n u m f u c t i o n ?

Commented by mr W last updated on 02/Mar/20

s i g n (x) = {\begin{cases} 1, i f x > 0 \\ 0, i f x = 0 \\ - 1, i f x < 0 \end{cases}

Answered by MJS last updated on 02/Mar/20

y = {\begin{cases} - x^{2}; x < 0 \\ x^{2}; x ⩾ 0 \end{cases}

y^{'} = {\begin{cases} - 2 x; x < 0 \\ 2 x; x ⩾ 0 \end{cases}

\Rightarrow y^{'} = 2 ∣ x ∣

Commented by jagoll last updated on 02/Mar/20

yes \dots my answer right . thank you mister

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