| 单词 | cross-partial derivative |
| 释义 | cross-partial derivative The effect of changing one argument of a function of two or more variables on the derivative of the function with respect to another argument. If y = f(x, z), the derivative, or first derivative, of y with respect to x is written ∂y/∂x = fx . If z changes, holding x constant, this may change fx. The second-order cross-partial is written fxz = ∂fx /∂z = ∂2 y/∂x∂z. For example, if y = (x + z)2 = x2 + 2xz + z2, fx = 2x + 2z, and fxz = 2. fzx is found in the same way, and is always equal to fxz (at least, for any function likely to appear in economics). By analogy, think of y as the height of land where x and z give position on a grid running North-South and East-West. The cross-partial gives the change in the North-South gradient as one moves in an East-West direction. |
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