Chapter 12 - Multi-Variate Calculus Applications; Partial Derivatives - HP 48gII User Manual

Chapter 12
Multi-variate Calculus Applications
Multi-variate calculus refers to functions of two or more variables.
Chapter we discuss basic concepts of multi-variate calculus: partial derivatives
and multiple integrals.

Partial derivatives

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. For example,
∂
(
x cos(
∂
x
•
You can use the derivative functions in the calculator: DERVX, DERIV,
∂, described in detail in Chapter 11 of this Guide, to calculate partial
derivatives (DERVX uses the CAS default variable VX, typically, 'X').
Some examples of first-order partial derivatives are shown next. The
functions used in the first two examples are f(x,y) = SIN(y), and
2
g(x,y,z) = (x +y
line. [Note: not all lines will be visible when done with the exercises
in the following figures.]
∂
) (
=
y ) cos( y ), x cos(
∂
y
2 1/2
) sin(z). Added the following note after this blank
)
= −
y ) x sin( y )
,
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