Higher-order derivatives, Higher-order derivatives ,14-3 – HP 50g Graphing Calculator User Manual
Page 463
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:
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
x
y
x
f
x
f
y
x
y
f
2
2
,
y
x
f
x
y
f
∂
∂
∂
=
∂
∂
∂
2
2