Answer
(a) $T_x(6,4)=3.5 ^\circ C/meter$ and $T_y(6,4)=-3.0 ^\circ C/meter$
(b) $D_uT(6,4)=1.1 ^\circ C/meter$
(c) $T_{xy}(6,4)=-0.25$
Work Step by Step
(a) $T_x(6,4)\approx \frac{T(8,4)-T(4,4)}{8-4}=\frac{86-72}{4}=3.5 ^\circ C/meter$
$T_y(6,4)\approx \frac{T(6,6)-T(6,2)}{6-2}=\frac{75-87}{4}=-3.0 ^\circ C/meter$
(b) $D_uT(6,4)\approx \frac{T(8,6)-T(4,2)}{\sqrt {(8-4)^2+(6-2)^2}}=\frac{80-74}{4\sqrt 2}=1.1 ^\circ C/meter$
(c) $T_{xy}(6,4)=\frac{T_x(6,6)-T_x(6,2)}{6-2}=\frac{3-4}{4}=-0.25$
