# Chapter 12 - Multi-variate Calculus Applications; Partial Derivatives - HP 50g User Manual

Graphing calculator.

Chapter 12
Multi-variate Calculus Applications
Multi-variate calculus refers to functions of two or more variables. In this
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(
y
)
cos(
y
),
x
cos(
y
)
x
sin(
y
)
x
y
,
You can use the derivative functions in the calculator: DERVX, DERIV, ,
described in detail in Chapter 11 of this manual, 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) = x cos(y), and g(x,y,z) =
2
2
1/2
(x
+y
)
sin(z).
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