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therefore, with DERVX you can only calculate derivatives with respect to X.
Some examples of first-order partial derivatives are shown next:
ʳʳʳʳʳ
Higher-order derivatives
The following second-order derivatives can be defined
The last two expressions represent cross-derivatives, the partial derivatives signs
in the denominator shows the order of derivation. In the left-hand side, the
derivation is taking first with respect to x and then with respect to y, and in the
right-hand side, the opposite is true. It is important to indicate that, if a
function is continuous and differentiable, then
.
,,
2
2
2
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
∂
∂
=
∂
∂
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
∂
∂
=
∂
∂
y
f
y
y
f
x
f
x
x
f
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
∂
∂
=
∂∂
∂
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
∂
∂
=
∂∂
∂
y
f
xyx
f
x
f
yxy
f
22
,
yx
f
xy
f
∂∂
∂
=
∂∂
∂
22