# y-x-2-2-x-1-3-2-Let-p-x-1-y-p-1-2p-3-2-Is-it-true-that-dy-dx-dy-dp-

Question Number 10956 by Joel576 last updated on 04/Mar/17
$${y}\:=\:\frac{{x}\:−\:\mathrm{2}}{\mathrm{2}\left({x}\:−\:\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} } \\$$$$\mathrm{Let}\:\:{p}\:=\:{x}\:−\:\mathrm{1} \\$$$$\Rightarrow\:{y}\:=\:\frac{{p}\:−\:\mathrm{1}}{\mathrm{2}{p}^{\mathrm{3}/\mathrm{2}} } \\$$$$\\$$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{true}\:\mathrm{that}\:\:\:\frac{{dy}}{{dx}}\:\:\:=\:\:\frac{{dy}}{{dp}}\:\:? \\$$
Commented by FilupS last updated on 04/Mar/17
$$\mathrm{if}\:{p}\:\mathrm{is}\:\mathrm{direct}\:\mathrm{substitution} \\$$$${f}\left({x}\right)={f}\left({p}\right) \\$$$$\therefore{f}\:'\left({x}\right)={f}\:'\left({p}\right) \\$$
Commented by Joel576 last updated on 04/Mar/17
$${thank}\:{you}\:{very}\:{much} \\$$
Commented by FilupS last updated on 04/Mar/17
$$\mathrm{only}\:\mathrm{if}\:\mathrm{you}\:\mathrm{substitute}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{values} \\$$$$\: \\$$$$\mathrm{e}.\mathrm{g}. \\$$$${p}={x}−\mathrm{1} \\$$$${f}\left({x}\right)\neq{f}\left({x}−\mathrm{1}\right)\:\Rightarrow\:\:\frac{{dy}}{{dx}}\neq\frac{{dy}}{{dp}}=\frac{{dy}}{{d}\left({x}−\mathrm{1}\right)} \\$$$$\mathrm{you}\:\mathrm{have}\:\mathrm{to}\:\mathrm{resubstitue}\:{x} \\$$
Commented by FilupS last updated on 04/Mar/17
$$\mathrm{if}\:{x}={g}\left({u}\right) \\$$$$\mathrm{and}\:{u}={h}\left({x}\right) \\$$$$\: \\$$$${y}={f}\left({x}\right) \\$$$${y}={g}\left({h}\left({x}\right)\right) \\$$$$\therefore\:\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}×\frac{{du}}{{dx}} \\$$