# HP 50g User Manual Page 462

Graphing calculator.

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
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
lim
x
h
0
f
lim
y
k
0
x
cos(
y
)
cos(
2
yx
x
f
(
x
h
,
y
)
f
h
f
(
x
,
y
k
)
f
k
y
),
x
cos(
y
2
y
2
yx
0
(
x
,
y
)
.
(
x
,
y
)
.
y
)
x
sin(
y
)
2
xy
,
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