Given-two-functions-f-x-and-g-x-with-f-1-7-g-2-1-f-1-204-and-g-x-22-What-is-the-derivative-of-f-g-x-at-x-2-

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

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

Answered by mrW1 last updated on 26/Apr/17

(df/dx)=((df(g))/dg)×((dg(x))/dx)=f′(g(x))×g′(x) =f′(g(2))×g′(2)=f′(1)×g′(2)=204×22 =4488

$$\frac{{df}}{{dx}}=\frac{{df}\left({g}\right)}{{dg}}×\frac{{dg}\left({x}\right)}{{dx}}={f}'\left({g}\left({x}\right)\right)×{g}'\left({x}\right) \\ $$$$={f}'\left({g}\left(\mathrm{2}\right)\right)×{g}'\left(\mathrm{2}\right)={f}'\left(\mathrm{1}\right)×{g}'\left(\mathrm{2}\right)=\mathrm{204}×\mathrm{22} \\ $$$$=\mathrm{4488} \\ $$

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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