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Question Number 195407 by mustafazaheen last updated on 01/Aug/23

$${\mathrm{f}}^{\prime }\left(2\right)={\mathrm{g}}^{\prime }\left(2\right)=\mathrm{g}\left(2\right)=2$$$$\mathrm{then}\mathrm{find}\mathrm{the}{\left(\mathrm{fog}\right)}^{\prime }\left(2\right)=?$$

Answered by gatocomcirrose last updated on 01/Aug/23

$${\left(\mathrm{fog}\right)}^{\prime }\left(2\right)={\mathrm{f}}^{\prime }\left(\mathrm{g}\left(2\right)\right){\mathrm{g}}^{\prime }\left(2\right)={2\mathrm{f}}^{\prime }\left(2\right)=4$$

Answered by sandy_delta last updated on 02/Aug/23

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

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