Menu Close

f-2-g-2-g-2-2-then-find-the-fog-2-




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

Leave a Reply

Your email address will not be published. Required fields are marked *