# HP 49g+ User Manual Page 459

Graphing calculator.

f
x
Similarly,
We will use the multi-variate functions defined earlier to calculate partial
derivatives using these definitions. Here are the derivatives of f(x,y) with
respect to x and y, respectively:
Notice that the definition of partial derivative with respect to x, for example,
requires that we keep y fixed while taking the limit as h 0. This suggest a
way to quickly calculate partial derivatives of multi-variate functions: use the
rules of ordinary derivatives with respect to the variable of interest, while
considering all other variables as constant. Thus, for example,
x
cos(
y
x
which are the same results as found with the limits calculated earlier.
Consider another example,
In this calculation we treat y as a constant and take derivatives of the
expression with respect to x.
Similarly, you can use the derivative functions in the calculator, e.g., DERVX,
DERIV, ∂ (described in detail in Chapter 13) to calculate partial derivatives.
Recall that function DERVX uses the CAS default variable VX (typically, 'X'),
f
(
x
h
,
y
)
f
lim
h
h
0
f
f
(
x
,
y
k
)
lim
y
k
k
0
)
cos(
y
),
x
cos(
y
2
2
yx
y
2
yx
0
x
(
x
,
y
)
.
f
(
x
,
y
)
.
y
)
x
sin(
y
)
,
2
xy
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