Hp 50g Graphing Calculator Manual do Utilizador descarregar pdf (Página 462)

100

101

Page 14-2

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,

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’),

yxfyhxf

),(),(

lim

−+

∂

→

yxfkyxf

),(),(

lim

−+

∂

→

() ()

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

yyx

−=

∂

()

xyyxyyx

202

=+=+

∂

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