HP 48gII Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 463)

100

101

Page 14-2

yxfyhxf

),(),(

lim

−+

∂

→

Similarly,

yxfkyxf

),(),(

lim

−+

∂

→

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,

() ()

)sin()cos(),cos()cos( yxyx

yyx

−=

∂

which are the same results as found with the limits calculated earlier.

Consider another example,

()

xyyxyyx

202

=+=+

∂

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’),

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