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

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

$$\left(\mathrm{f}\:\bullet\:\mathrm{g}\right)'\left(\mathrm{2}\right)=\left(\mathrm{g}'\bullet\:\mathrm{f}\:'\right)\left(\mathrm{2}\right) \\ $$$$=\:\mathrm{g}'\left[\mathrm{f}\:'\left(\mathrm{2}\right)\right]=\:\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{2} \\ $$

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