Question Number 131007 by Study last updated on 31/Jan/21
$$\frac{{d}}{{dx}}\left(\infty\right)=?\:\:\:\:\:{or}\:\:\:\left(\infty\right)'=? \\ $$
Answered by Boucatchou last updated on 31/Jan/21
$$\infty\:{is}\:{unknown},\:{so}\:\:{they}\:\:{can}'{t}\:\:{do}\:\:{such}\:\:{operations}.. \\ $$
Answered by MJS_new last updated on 31/Jan/21
$${x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{variable},\:\infty\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\:\Rightarrow\:\infty'=\mathrm{0} \\ $$
Commented by MJS_new last updated on 31/Jan/21
![f(x)=c (d/dx)[lim_(c→∞) c]=0](https://www.tinkutara.com/question/Q131015.png)
$${f}\left({x}\right)={c} \\ $$$$\frac{{d}}{{dx}}\left[\underset{{c}\rightarrow\infty} {\mathrm{lim}}\:{c}\right]=\mathrm{0} \\ $$
Commented by JDamian last updated on 31/Jan/21
$${But}\:\:\infty\:\:{is}\:{not}\:{a}\:{number} \\ $$
Commented by MJS_new last updated on 31/Jan/21
![but (d/dx)[anything without x]=0](https://www.tinkutara.com/question/Q131030.png)
$$\mathrm{but}\:\frac{{d}}{{dx}}\left[{anything}\:{without}\:\mathrm{x}\right]=\mathrm{0} \\ $$
Commented by Boucatchou last updated on 31/Jan/21
![They know R^ =[−∞; ∞], so, where is (d/dx)(∞)=0 ? in R or in R^ ?](https://www.tinkutara.com/question/Q131047.png)
$${They}\:{know}\:\:\bar {\mathbb{R}}=\left[−\infty;\:\infty\right],\:{so},\:{where}\:{is}\:\:\frac{{d}}{{dx}}\left(\infty\right)=\mathrm{0}\:?\:\:{in}\:\mathbb{R}\:\:{or}\:\:{in}\:\:\bar {\mathbb{R}}\:? \\ $$
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](https://www.tinkutara.com/question/Q131051.png)
$$\frac{{d}}{{dx}}\left[{term}\:{without}\:{x}\right]=\mathrm{0} \\ $$$$\mathrm{if}\:\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{clear},\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{help} \\ $$