Suppose we take the partial derivative
∂
∂
x
[
f
(
x
,
y
,
z
)
]
\displaystyle {\frac{{\partial}}{{\partial{x}}}}{\left[{f{{\left({x},{y},{z}\right)}}}\right]}
∂
x
∂
[
f
(
x
,
y
,
z
)
]
. Graphically, in which direction are we moving? (Which axis are we moving parallel to?)
In the
−
x
\displaystyle -{x}
−
x
direction (parallel to the
x
\displaystyle {x}
x
-axis).
In the
+
z
\displaystyle +{z}
+
z
direction (parallel to the
z
\displaystyle {z}
z
-axis).
In the
−
z
\displaystyle -{z}
−
z
direction (parallel to the
z
\displaystyle {z}
z
-axis).
In the
+
y
\displaystyle +{y}
+
y
direction (parallel to the
y
\displaystyle {y}
y
-axis).
In the
−
y
\displaystyle -{y}
−
y
direction (parallel to the
y
\displaystyle {y}
y
-axis).
In the
+
x
\displaystyle +{x}
+
x
direction (parallel to the
x
\displaystyle {x}
x
-axis).
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