Question Number 201798 by hardmath last updated on 12/Dec/23
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\boldsymbol{\mathrm{y}}\:=\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$
Answered by dimentri last updated on 12/Dec/23
$$\:{y}=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\Rightarrow{y}'=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\frac{{x}}{{y}} \\ $$$$\:{yy}'−{x}\:=\:\mathrm{0}\: \\ $$