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Question-108949




Question Number 108949 by mohammad17 last updated on 20/Aug/20
Commented by kaivan.ahmadi last updated on 20/Aug/20
z_x =(1/( (√(1−(x+e^(√(y−1)) )^2 )))).tan(xy)+y(1+tan^2 (xy)).sin^(−1) (x+e^(√(y−1)) )  ⇒z_x (1,1)=(1/( (√(−3))))tan1+(1+tan^2 1)sin^(−1) (2)  is not defined, since (1,1)∉D_z_x    .
$${z}_{{x}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\left({x}+{e}^{\sqrt{{y}−\mathrm{1}}} \right)^{\mathrm{2}} }}.{tan}\left({xy}\right)+{y}\left(\mathrm{1}+{tan}^{\mathrm{2}} \left({xy}\right)\right).{sin}^{−\mathrm{1}} \left({x}+{e}^{\sqrt{{y}−\mathrm{1}}} \right) \\ $$$$\Rightarrow{z}_{{x}} \left(\mathrm{1},\mathrm{1}\right)=\frac{\mathrm{1}}{\:\sqrt{−\mathrm{3}}}{tan}\mathrm{1}+\left(\mathrm{1}+{tan}^{\mathrm{2}} \mathrm{1}\right){sin}^{−\mathrm{1}} \left(\mathrm{2}\right) \\ $$$${is}\:{not}\:{defined},\:{since}\:\left(\mathrm{1},\mathrm{1}\right)\notin{D}_{{z}_{{x}} } \:\:. \\ $$

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