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Question Number 131007 by Study last updated on 31/Jan/21

(d/dx)(∞)=? or (∞)′=?

$$\frac{{d}}{{dx}}\left(\infty\right)=?\:\:\:\:\:{or}\:\:\:\left(\infty\right)'=? \\ $$

Answered by Boucatchou last updated on 31/Jan/21

∞ is unknown, so they can′t do such operations..

$$\infty\:{is}\:{unknown},\:{so}\:\:{they}\:\:{can}'{t}\:\:{do}\:\:{such}\:\:{operations}.. \\ $$

Answered by MJS_new last updated on 31/Jan/21

x is the variable, ∞ is a constant ⇒ ∞′=0

$${x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{variable},\:\infty\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\:\Rightarrow\:\infty'=\mathrm{0} \\ $$

Commented by MJS_new last updated on 31/Jan/21

f(x)=c (d/dx)[lim_(c→∞) c]=0

$${f}\left({x}\right)={c} \\ $$$$\frac{{d}}{{dx}}\left[\underset{{c}\rightarrow\infty} {\mathrm{lim}}\:{c}\right]=\mathrm{0} \\ $$

Commented by JDamian last updated on 31/Jan/21

But ∞ is not a number

$${But}\:\:\infty\:\:{is}\:{not}\:{a}\:{number} \\ $$

Commented by MJS_new last updated on 31/Jan/21

but (d/dx)[anything without x]=0

$$\mathrm{but}\:\frac{{d}}{{dx}}\left[{anything}\:{without}\:\mathrm{x}\right]=\mathrm{0} \\ $$

Commented by Boucatchou last updated on 31/Jan/21

They know R^� =[−∞; ∞], so, where is (d/dx)(∞)=0 ? in R or in R^� ?

$${They}\:{know}\:\:\bar {\mathbb{R}}=\left[−\infty;\:\infty\right],\:{so},\:{where}\:{is}\:\:\frac{{d}}{{dx}}\left(\infty\right)=\mathrm{0}\:?\:\:{in}\:\mathbb{R}\:\:{or}\:\:{in}\:\:\bar {\mathbb{R}}\:? \\ $$

Commented by MJS_new last updated on 01/Feb/21

(d/dx)[term without x]=0 if this is not clear, I can′t help

$$\frac{{d}}{{dx}}\left[{term}\:{without}\:{x}\right]=\mathrm{0} \\ $$$$\mathrm{if}\:\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{clear},\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{help} \\ $$

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