Question Number 108949 by mohammad17 last updated on 20/Aug/20
Commented by kaivan.ahmadi last updated on 20/Aug/20
$${z}_{{x}} =\frac{\mathrm{1}}{\sqrt{\mathrm{1}−\left({x}+{e}^{\sqrt{{y}−\mathrm{1}}} \right)^{\mathrm{2}} }}.{tan}\left({xy}\right)+{y}\left(\mathrm{1}+{tan}^{\mathrm{2}} \left({xy}\right)\right).{sin}^{−\mathrm{1}} \left({x}+{e}^{\sqrt{{y}−\mathrm{1}}} \right) \\ $$$$\Rightarrow{z}_{{x}} \left(\mathrm{1},\mathrm{1}\right)=\frac{\mathrm{1}}{\sqrt{−\mathrm{3}}}{tan}\mathrm{1}+\left(\mathrm{1}+{tan}^{\mathrm{2}} \mathrm{1}\right){sin}^{−\mathrm{1}} \left(\mathrm{2}\right) \\ $$$${is}\:{not}\:{defined},\:{since}\:\left(\mathrm{1},\mathrm{1}\right)\notin{D}_{{z}_{{x}} } \:\:. \\ $$