Set F=xy−z log y+e^(xz)−1. At the point, F_x=y+ze^(xz)=2,F_y=x−z/y=−1 and F_z=−log y+xe^(xz)=0. Since F_y≠0, the implicit function theorem applies and (f_x,f_z)=−(F_x,F_z)/F_y=**(2,0), A**.
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