HP 48gII - Manual (Page 464)

Page 14-3
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
, ,
2
2
2
2




∂
∂
∂
∂
=
∂
∂






∂
∂
∂
∂
=
∂
∂
y
f
y y
f
x
f
x x
f




∂
∂
∂
∂
=
∂ ∂
∂






∂
∂
∂
∂
=
∂ ∂
∂
y
f
x y x
f
x
f
y x y
f 2 2
,
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
y x
f
x y
f
∂ ∂
∂
=
∂ ∂
∂ 2 2
.