Question Number 203169 by hardmath last updated on 11/Jan/24
$$\mathrm{If}\:\:\:\mathrm{y}\:=\:\mathrm{tan} \\ $$$$\mathrm{Find}\:\:\:\mathrm{y}^{'} \:=\:? \\ $$
Answered by a.lgnaoui last updated on 11/Jan/24
$$\mathrm{y}'=\frac{\mathrm{cos}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} }{\mathrm{cos}\:^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} }=\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \\ $$$$\:\:\mathrm{donc}\:\:\:\mathrm{y}'=\mathrm{1}+\mathrm{y}^{\mathrm{2}} \: \\ $$