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Question Number 12576 by tawa last updated on 26/Apr/17

$$\mathrm{Given}\mathrm{two}\mathrm{functions}\mathrm{f}\left(\mathrm{x}\right)\mathrm{and}\mathrm{g}\left(\mathrm{x}\right)\mathrm{with}\mathrm{f}\left(1\right)=7,\mathrm{g}\left(2\right)=1,{\mathrm{f}}^{\prime }\left(1\right)=204$$$$\mathrm{and}{\mathrm{g}}^{\prime }\left(\mathrm{x}\right)=22.\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{derivative}\mathrm{of}\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\mathrm{at}\mathrm{x}=2$$

Answered by mrW1 last updated on 26/Apr/17

$$\frac{df}{dx}=\frac{df\left(g\right)}{dg}\times \frac{dg\left(x\right)}{dx}=f^{\prime }\left(g\left(x\right)\right)\times g^{\prime }\left(x\right)$$$$=f^{\prime }\left(g\left(2\right)\right)\times g^{\prime }\left(2\right)=f^{\prime }\left(1\right)\times g^{\prime }\left(2\right)=204\times 22$$$$=4488$$

Commented by tawa last updated on 26/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by tawa last updated on 26/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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