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f-x-x-3-3-x-2-4-16-g-x-f-x-2-1-find-g-2-




Question Number 135393 by Eric002 last updated on 12/Mar/21
f ′(x)=(((x−3)^3 (x^2 −4))/(16))  g(x)=f(x^2 −1)  find g′(2)
$${f}\:'\left({x}\right)=\frac{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{4}\right)}{\mathrm{16}} \\ $$$${g}\left({x}\right)={f}\left({x}^{\mathrm{2}} −\mathrm{1}\right) \\ $$$${find}\:{g}'\left(\mathrm{2}\right) \\ $$
Answered by MJS_new last updated on 12/Mar/21
g′(x)=2xf′(x^2 −1) ⇒ g′(2)=0
$${g}'\left({x}\right)=\mathrm{2}{xf}'\left({x}^{\mathrm{2}} −\mathrm{1}\right)\:\Rightarrow\:{g}'\left(\mathrm{2}\right)=\mathrm{0} \\ $$

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