Question Number 195407 by mustafazaheen last updated on 01/Aug/23
$$\mathrm{f}'\left(\mathrm{2}\right)=\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{g}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=? \\ $$
Answered by gatocomcirrose last updated on 01/Aug/23
$$\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=\mathrm{f}'\left(\mathrm{g}\left(\mathrm{2}\right)\right)\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{2f}'\left(\mathrm{2}\right)=\mathrm{4} \\ $$
Answered by sandy_delta last updated on 02/Aug/23
![(f • g)′(2)=(g′• f ′)(2) = g′[f ′(2)]= g′(2)=2](Q195462.png)
$$\left(\mathrm{f}\:\bullet\:\mathrm{g}\right)'\left(\mathrm{2}\right)=\left(\mathrm{g}'\bullet\:\mathrm{f}\:'\right)\left(\mathrm{2}\right) \\ $$$$=\:\mathrm{g}'\left[\mathrm{f}\:'\left(\mathrm{2}\right)\right]=\:\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{2} \\ $$