Suppose
f
(
x
,
y
,
z
)
\displaystyle {f{{\left({x},{y},{z}\right)}}}
f
(
x
,
y
,
z
)
is a function of three variables. In what order is the notation
f
z
y
y
\displaystyle {f}_{{{z}{y}{y}}}
f
z
y
y
telling us to differentiate
f
\displaystyle {f}
f
?
With respect to
y
\displaystyle {y}
y
first, then
y
\displaystyle {y}
y
again, and then
z
\displaystyle {z}
z
.
With respect to
x
\displaystyle {x}
x
first, then
y
\displaystyle {y}
y
, and then
z
\displaystyle {z}
z
.
With respect to
z
\displaystyle {z}
z
first, then
y
\displaystyle {y}
y
, and then
y
\displaystyle {y}
y
again.
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