Higher-Order Derivatives - HP 50g User Manual

therefore, with DERVX you can only calculate derivatives with respect to X.
Some examples of first-order partial derivatives are shown next:

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
f f
⎛ ⎞
⎜ ⎟
2
x x x
⎝ ⎠
2
f f
⎛ ⎞
⎜ ⎟
y x y x
⎝ ⎠
2
f
y x
2
⎛
f
⎜ ⎜
,
2
y y
⎝
2 ⎛
f
, ⎜ ⎜
x y x
⎝
2
f
.
x y
⎞
f
⎟ ⎟
,
y
⎠
⎞
f
⎟ ⎟
y
⎠
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