HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 463

Similarly, ∂f = lim f (x + h, y) − f (x, y) . ∂x h→0 h ∂f = lim f (x, y + k) − f (x, y) . ∂y k→0 k 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, ∂ (x cos( y)) = cos( y), ∂ (x cos( y)) = −x sin( y) , ∂x ∂y which are the same results as found with the limits calculated earlier. Consider another example, ( ) ∂ yx2 + y 2 = 2 yx + 0 = 2xy ∂x 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'), Page 14-2