Question Number 118065 by andilizhaa last updated on 15/Oct/20
Answered by bobhans last updated on 15/Oct/20
$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{1}−\mathrm{cot}\:\mathrm{x} \\ $$$$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}\:=\:\mathrm{cosec}\:^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}\mid_{\frac{\pi}{\mathrm{6}}} \:=\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{6}}\right)}\:=\:\mathrm{4} \\ $$