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Question Number 11571 by Nayon last updated on 28/Mar/17

$${why}\:\:\:\frac{{d}\left[{f}\left\{{g}\left({x}\right)\right\}\right]}{{dx}}=\frac{{df}\left[\left\{{g}\left({x}\right)\right\}\right]}{{dg}\left({x}\right)}.\frac{{dg}\left({x}\right)}{{dx}}? \\ $$

Answered by mrW1 last updated on 28/Mar/17

y=f(u) u=g(x) (dy/dx)=(dy/du)×(du/dx) ⇒ ((d[f{g(x)}])/dx)=((df[{g(x)}])/(dg(x))).((dg(x))/dx)

$${y}={f}\left({u}\right) \\ $$$${u}={g}\left({x}\right) \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}×\frac{{du}}{{dx}} \\ $$$$\Rightarrow\:\frac{{d}\left[{f}\left\{{g}\left({x}\right)\right\}\right]}{{dx}}=\frac{{df}\left[\left\{{g}\left({x}\right)\right\}\right]}{{dg}\left({x}\right)}.\frac{{dg}\left({x}\right)}{{dx}} \\ $$$$ \\ $$

Commented by mrW1 last updated on 28/Mar/17