HP 49g Partial derivatives, ∂∂x (x cos( y)) = cos( y), ∂∂y (x cos( y)) = −x sin( y)

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 (x cos( y)) = cos( y), ∂∂y (x cos( y)) = −x sin( 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 two examples are f(x,y) = SIN(y), and g(x,y,z) = (x2+y2)1/2sin(z).

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