The Mixed Partial Derivative Theorem allows us to write
D
\displaystyle {D}
D
(in the the Second Derivative Test) as either
D
(
x
,
y
)
=
(
f
x
x
)
(
f
y
y
)
−
(
f
x
y
)
2
\displaystyle {D}{\left({x},{y}\right)}={\left({f}_{{{x}{x}}}\right)}{\left({f}_{{{y}{y}}}\right)}-{\left({f}_{{{x}{y}}}\right)}^{{2}}
D
(
x
,
y
)
=
(
f
x
x
)
(
f
y
y
)
−
(
f
x
y
)
2
or
D
(
x
,
y
)
=
(
f
x
x
)
(
f
y
y
)
−
(
f
y
x
)
2
\displaystyle {D}{\left({x},{y}\right)}={\left({f}_{{{x}{x}}}\right)}{\left({f}_{{{y}{y}}}\right)}-{\left({f}_{{{y}{x}}}\right)}^{{2}}
D
(
x
,
y
)
=
(
f
x
x
)
(
f
y
y
)
−
(
f
y
x
)
2
.
True
False
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