Chapter 12 - Multi-Variate Calculus Applications; Partial Derivatives - HP 49g+ User Manual

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 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
2 2 1/2
two examples are f(x,y) = SIN(y), and g(x,y,z) = (x +y ) sin(z).
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