Question Number 75402 by vishalbhardwaj last updated on 10/Dec/19
$$\mathrm{Explain}\:\mathrm{the}\:\mathrm{proof}\: \\ $$$$\mathrm{with}\:\mathrm{appropriate} \\ $$$$\mathrm{diagram}\::\: \\ $$$$\mathrm{Lim}_{{h}\rightarrow\mathrm{0}} \frac{{f}\left({x}\right)−{f}\left({x}−{h}\right)}{−{h}}\: \\ $$$$\:\:\:=\:\frac{{dy}}{{dx}}\:,\:\mathrm{where}\:{y}\:=\:{f}\left({x}\right) \\ $$
Commented by Kunal12588 last updated on 10/Dec/19
$${isn}'{t}\:{it}\:{the}\:{defination}\:{of}\:{derivative}? \\ $$$${first}\:{principle} \\ $$$$\frac{{dy}}{{dx}}=\underset{\Delta{x}\rightarrow\mathrm{0}} {{lim}}\frac{\Delta{y}}{\Delta{x}}=\underset{\Delta{x}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)}{\Delta{x}} \\ $$
Commented by vishalbhardwaj last updated on 10/Dec/19
$$\mathrm{sir}\:\:\mathrm{this}\:\mathrm{is}\:\mathrm{LHD} \\ $$
Commented by Kunal12588 last updated on 10/Dec/19
$$\Delta{x}=\mathrm{0}−{h} \\ $$$$\Rightarrow\Delta{x}=−{h} \\ $$$$\Delta{x}\rightarrow\mathrm{0}\Rightarrow{h}\rightarrow\mathrm{0} \\ $$$${LHD}=\underset{{h}\rightarrow\mathrm{0}} {{lim}}\:\frac{{f}\left({x}−{h}\right)−{f}\left({x}\right)}{−{h}} \\ $$
Commented by vishalbhardwaj last updated on 12/Dec/19
$$\mathrm{please}\:\mathrm{explain}\:\mathrm{the}\:\mathrm{proof}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{diagram} \\ $$